A nonlift newform <i>f</i> in S

A nonlift newform in S₁₄(K(16))⁺

(Filename: eigs/eig-plus-14-16-4.html)

FORMULA FOR THE EIGENFORM f
with 3¹⁴⁻³λ₃ = 969288 + 7680*α,
where throughout this wepage, α is taken to have minimal polynomial -25561 + x^2

Note that T(3) is the Hecke operator under the scalar-invariant slash and λ₃ is the corresponding eigenvalue.

The eigenform f has the formula
f = Σ_i=1¹⁴ b_i Grit(φ_i) + Σ_i=0⁵⁹ c_1,i T(3)ⁱ g₁ + Σ_i=0⁵⁹ c_2,i T(3)ⁱ g₂ + Σ_i=0⁵⁹ c_4,i T(3)ⁱ g₄
where g₁, g₂, g₄ are the Borcherds products that helped span the space S₁₄(K(16))⁺ and where φ_i are jacobi forms in J_14,16^cusp given by the following table.

φ₁	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,4)\|W₂
φ₂	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2)\|W₂
φ₃	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,6)\|W₃
φ₄	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,4,4)\|W₃
φ₅	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,6)\|W₃
φ₆	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4)\|W₃
φ₇	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3)\|W₃
φ₈	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3)\|W₃
φ₉	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,10)\|W₅
φ₁₀	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,7,8)\|W₅
φ₁₁	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4,5,8)\|W₅
φ₁₂	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,5,5,8)\|W₅
φ₁₃	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,5,6,6)\|W₅
φ₁₄	TB(14;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,4,4,4,4,4,5,5)\|W₅

Here is a table of the coefficients b_i and c_j,i.

b₁	1030716621568570122271126038898171872545101570225931112117026247528622399054658409824136984396499011869538210347004107523608077863402723826247847142626916707570459699148305813026374860596151208470793291245201226957988803822672430476871518301427488975788738687855933675544417666116229938256714861242120516877854833946512427227432837947499143320349873874378037576900165663980175257605957244262064381422742765818205623401434816816361933198209026592806561/917774134971849084496377981681436063204516408231485885557471647819378422578547269445231287843484601257324800371552894438616667597785372923568931050989392502089523471134335927566538406393073475881578578230110389809951841799358590025206666220035279422422490794467196324738339431964156057977483612621039962388897103871971581840971209546203733848140823150428605209030651974655414218631719600605351309340870411319881132931022848000000 - (6446891474638037642199663165788741940692403164069834588577557546683040752625041996950121178164407308720661473293306320609462392781331312206790931766456677540078976069883034485808549029493562750410644656761616598281577183422445375165657778149109432160295725178244929114664881269191963220490426204764808564992922090440145956871354645141651026090145007911963212263395070822952703406511793821740661094886662805166587092038254922454309154552685969873971*α)/917774134971849084496377981681436063204516408231485885557471647819378422578547269445231287843484601257324800371552894438616667597785372923568931050989392502089523471134335927566538406393073475881578578230110389809951841799358590025206666220035279422422490794467196324738339431964156057977483612621039962388897103871971581840971209546203733848140823150428605209030651974655414218631719600605351309340870411319881132931022848000000
b₂	-3091319983868146241587555189142348860628148256256949780002832388668606675845016653491577579293676869577296650205185866763096987216347456269662693667679875551147189516678806177015048377441425541315396476953363427145730813991524213360553113989726413784867375895533263277103209151341810984151715813736790260830822124665947781875172793925854069831996744407654010517420636354407681432870047702754463708322576117397080157854182530588377721474811741219647477/2294435337429622711240944954203590158011291020578714713893679119548446056446368173613078219608711503143312000928882236096541668994463432308922327627473481255223808677835839818916346015982683689703946445575275974524879604498396475063016665550088198556056226986167990811845848579910390144943709031552599905972242759679928954602428023865509334620352057876071513022576629936638535546579299001513378273352176028299702832327557120000000 + (19335483713310731330298807235490113561528924285610604765149009317644660150514898060271662430236684993829118052217155341677166124790652609278515812283093263334055468077136943122241710722502509408831739529538451413289792381775000963437631381892931862500892721778347577531246157523636873734822915386457707296127535950673659742585578241773226167281605879714824994199121958770880803551099405230957224818865410618160213617724659566931038737508415155636847*α)/2294435337429622711240944954203590158011291020578714713893679119548446056446368173613078219608711503143312000928882236096541668994463432308922327627473481255223808677835839818916346015982683689703946445575275974524879604498396475063016665550088198556056226986167990811845848579910390144943709031552599905972242759679928954602428023865509334620352057876071513022576629936638535546579299001513378273352176028299702832327557120000000
b₃	18000769363611820013691709032835509869860336166836631716165409732464670386685874598205358827008536979331538154689639731046470601491521851229845720496423953953571626493752116862376499914835717311078335836008383953337032509211387913546208310949914418340912130566926204596757374695257608654805313283627030575893285170682091893624820785979812449279644021091983446412184368684970845499416024556443839690969215711492066852990349534741248816632911218183717/9975805814911403092351934583493870252223004437298759625624691824123678506288557276578600954820484796275269569256009722158876821715058401343140554902058614153146994251460173125723243547750798650886723676414243367499476541297375978534855067609079124156766204287686916573242819912653870195407430571967825678140185911651865020010556625502214498349356773374223969663376651898428415419909995658753818579792069688259577531858944000000 - (2589583882448244870415179013632133768456337605399341302801280794654038024299400929480179504767378721127427080516745201978247458598074667401119137712990669978438964571974619438317754830008894564762535065288224804158470973103739413294177447300749581147354036007305428235718029880820289150255376242636119580889375711997906859620695373352444763957198180950396949893178400262540890432031055844338963642653553798040718419231760225695226012697667957812201*α)/229443533742962271124094495420359015801129102057871471389367911954844605644636817361307821960871150314331200092888223609654166899446343230892232762747348125522380867783583981891634601598268368970394644557527597452487960449839647506301666555008819855605622698616799081184584857991039014494370903155259990597224275967992895460242802386550933462035205787607151302257662993663853554657929900151337827335217602829970283232755712000000
b₄	534809437795938117466073866162197733207857406252615596457367159938589060090093129753405892009429831149874197939272540382851771308673231268610030663798054534878419530731697165266854306223016901761775394675552195946438265326754976498478396633215173822424344244044179840968295237174272588030906318421973443121257105509508679082930239015991145889031333228171887596662028512343392057425671310750294229833485080934380083229522504364725241449076363638878493/294998829098094348588121494111890163172880274074406177500615886799085921543104479464538628235405764689854400119427716069555357442145298439718584980675161875671632544293179405289244487769202188676221685859678339581770234864079546793816428427868482671492943469650170247237323388845621590064191161199619987910716926244562294163169317354136914451188121726923480245759852420424954570274481300194577206573851203638533221299257344000000 - (3345107988882103120552703726463673924402046787286684923375179755250152656000741700041140324303705700159789717131489053123294494914018693599023894805783310664216756169427302013718821625824335550146749004732080849767907826610592478401962804064556189192143664249142988028935313767085516660424572963849299383455365720250062761449149718470763143812671934496416669619877156984411677786336388395110513625621683045606953644086247300563541743477371906398823*α)/294998829098094348588121494111890163172880274074406177500615886799085921543104479464538628235405764689854400119427716069555357442145298439718584980675161875671632544293179405289244487769202188676221685859678339581770234864079546793816428427868482671492943469650170247237323388845621590064191161199619987910716926244562294163169317354136914451188121726923480245759852420424954570274481300194577206573851203638533221299257344000000
b₅	5822263641453529178170386262253542870463232109027162511108373115253457416950911535627388489883953388918385014505711651700890573852147155834473128796921695557703736299121998565170910432017732965710902466354938181609696671907911765167801585430013234976832706218320558907586769919672456421781622882181582854358262201429766377638508942840000513512282567359344494241639438788444240289180087656140124268072818183598356846343890550409781947440586878178941817/2477990164423992528140220550539877370652194302225011891005173449112321740962077627502124477177408423394776961003192814984265002514020506893636113837671359755641713372062707004429653697261298384880262161221298052486869972858268193068057998794095254440540725145061430076793516466303221356539205754076807898450022180454323270970622265774750081389980222506157234064382760331569618390305642921634448535220350110563679058913761689600000 - (36416897765808138235645208492059141948726764673987507590380824653124483581363734115952810535478499577450093237094269786183313559731423803357293377991954804876471356789658331879384480596330236394676214825560524630584943994128823509740079012663575516443285244441849962001746710574888914312185694041901994909017438222109962563010807018931335948459250765904922272797481660672700143068432318460600830473359017641911988026978835315718538255755002173193787*α)/2477990164423992528140220550539877370652194302225011891005173449112321740962077627502124477177408423394776961003192814984265002514020506893636113837671359755641713372062707004429653697261298384880262161221298052486869972858268193068057998794095254440540725145061430076793516466303221356539205754076807898450022180454323270970622265774750081389980222506157234064382760331569618390305642921634448535220350110563679058913761689600000
b₆	14338092329508295377534016608162360798069424706445738456946534309292046192231801961323429147765123332900011430271109388032601545827092460646780750055973396950781518315627720987981664037331847511092882482708583855692963758063160408980950883187304266938595250909383043830102518623666439834760167261900755817122765925425246453206397931150941648377737248770080902364547823312974106400536223169350524073653767565356418927295887813916659406021818928977660043/9530731401630740492847002117461066810200747316250045734635282496585852849854144721162017219913109320749142157704587749939480778900078872667831207067966768290929666815625796170883283451004993788001008312389607894180269126377954588723299995361904824771310481327159346449205832562704697525150791361833876532500085309439704888348547176056731082269154701946758592555318308967575455347329395852440186673924423502167996380437544960000000 - (89681415111952383612076808462408799428196830042431807706754977451063783481653302189634533045190910466590123793959442716316371620679463250070233024031420405891132877887943441938094273837687706426109914796411466846155908914571670426019472410719785061742113620968357583039336805358822919534033340594443699904803367180142519258098546681577668797168179863491656545650304072795412936014292697749587420151205555207515740811214888891258078019170534220121873*α)/9530731401630740492847002117461066810200747316250045734635282496585852849854144721162017219913109320749142157704587749939480778900078872667831207067966768290929666815625796170883283451004993788001008312389607894180269126377954588723299995361904824771310481327159346449205832562704697525150791361833876532500085309439704888348547176056731082269154701946758592555318308967575455347329395852440186673924423502167996380437544960000000
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c_1,40	-167751086405668708940996104790951649921484057400917689412878622326862679644275352107053024938657381440033457339237886678300068264974518791040514440399950854334772980879942991814920343610115454774292997191788640256396234179316525823159034054813582247611316249133702822611056674599037650975642161295783344390591021290184077999542931/162324167083716230624561929039382179372203858016455905135980840060500358243149998823563801715689111648068400829220323756264401519630352369698332218939540113210280762717460279540737758548886225775276427574945520812885940592659962693784330088805862233140838266757795991708562191502953346802342230544083207017921704019224665032590114678733851852800000000 + (1049243823354824627065864969752767354675136353478042275505356553386588782513392521043162004416261077238987047139137111976436793528656858958126927267589714777430403461009205431836200901603338236389478907109355616174014452916713862959626838647148552553285228730614206518207781428559432009814852933322465805054200999486210653897641*α)/162324167083716230624561929039382179372203858016455905135980840060500358243149998823563801715689111648068400829220323756264401519630352369698332218939540113210280762717460279540737758548886225775276427574945520812885940592659962693784330088805862233140838266757795991708562191502953346802342230544083207017921704019224665032590114678733851852800000000
c_1,41	11214993875595794506814233062584204443170273835082949410878522723843087605192010384468589566341830824758211427662381963538153701389250682024032467564317094533808026853190229124611981456586903074231815117931763665508826788974995098390184564633743202360524182569885117529468522396387951342766436943476814136433587437426021221505439561/135053707013651903879635524960765973237673609869691313073136058930336298058300799021205083027453340891192909489911309365211982064332453171589012406157697374190953594580926952577893815112673339845029987742354673316321102573093088961228562633886477377973177437942486265101523743330457184539548735812677228238910857743994921307114975412706564741529600000000 - (70147164498682078233613144344945330472566678115098478829755156205680626898870194475578173566033452242613690347601831469378781761035490064690069071031665441566742981614136871455468152789582392529592650894325510224615463148147764042683641626347836709637359116234930793756384080326235238059285784045171047323972517229320904042816171*α)/135053707013651903879635524960765973237673609869691313073136058930336298058300799021205083027453340891192909489911309365211982064332453171589012406157697374190953594580926952577893815112673339845029987742354673316321102573093088961228562633886477377973177437942486265101523743330457184539548735812677228238910857743994921307114975412706564741529600000000
c_1,42	0
c_1,43	0
c_1,44	0
c_1,45	0
c_1,46	0
c_1,47	0
c_1,48	0
c_1,49	0
c_1,50	0
c_1,51	0
c_1,52	0
c_1,53	0
c_1,54	0
c_1,55	0
c_1,56	0
c_1,57	0
c_1,58	0
c_1,59	0
c_2,0	0
c_2,1	0
c_2,2	0
c_2,3	0
c_2,4	0
c_2,5	0
c_2,6	0
c_2,7	0
c_2,8	0
c_2,9	0
c_2,10	0
c_2,11	0
c_2,12	0
c_2,13	0
c_2,14	0
c_2,15	0
c_2,16	0
c_2,17	0
c_2,18	0
c_2,19	0
c_2,20	0
c_2,21	0
c_2,22	0
c_2,23	0
c_2,24	0
c_2,25	0
c_2,26	0
c_2,27	0
c_2,28	0
c_2,29	0
c_2,30	0
c_2,31	0
c_2,32	0
c_2,33	0
c_2,34	0
c_2,35	0
c_2,36	0
c_2,37	0
c_2,38	0
c_2,39	0
c_2,40	0
c_2,41	0
c_2,42	0
c_2,43	0
c_2,44	0
c_2,45	0
c_2,46	0
c_2,47	0
c_2,48	0
c_2,49	0
c_2,50	0
c_2,51	0
c_2,52	0
c_2,53	0
c_2,54	0
c_2,55	0
c_2,56	0
c_2,57	0
c_2,58	0
c_2,59	0
c_4,0	0
c_4,1	0
c_4,2	0
c_4,3	0
c_4,4	0
c_4,5	0
c_4,6	0
c_4,7	0
c_4,8	0
c_4,9	0
c_4,10	0
c_4,11	0
c_4,12	0
c_4,13	0
c_4,14	0
c_4,15	0
c_4,16	0
c_4,17	0
c_4,18	0
c_4,19	0
c_4,20	0
c_4,21	0
c_4,22	0
c_4,23	0
c_4,24	0
c_4,25	0
c_4,26	0
c_4,27	0
c_4,28	0
c_4,29	0
c_4,30	0
c_4,31	0
c_4,32	0
c_4,33	0
c_4,34	0
c_4,35	0
c_4,36	0
c_4,37	0
c_4,38	0
c_4,39	0
c_4,40	0
c_4,41	0
c_4,42	0
c_4,43	0
c_4,44	0
c_4,45	0
c_4,46	0
c_4,47	0
c_4,48	0
c_4,49	0
c_4,50	0
c_4,51	0
c_4,52	0
c_4,53	0
c_4,54	0
c_4,55	0
c_4,56	0
c_4,57	0
c_4,58	0
c_4,59	0

COEFFICIENTS OF f (return to top)

Use the notation

[a b c ]

a	b
b	c

Here is a list of some Fourier coefficients of f.

2u det(2u) a(u, f)

[4 -53 704] 7 -588949/90365118382080 + (4499*α)/90365118382080

[8 -89 992] 15 21009787/6024341225472 - (42399*α)/2008113741824

[4 -25 160] 15 -17725811/10040568709120 + (404143*α)/30121706127360

[12 -109 992] 23 1695660967/90365118382080 - (6703697*α)/90365118382080

[6 -13 32] 23 1695660967/90365118382080 - (6703697*α)/90365118382080

[6 -19 64] 23 -2993781401/90365118382080 + (21570991*α)/90365118382080

[14 -42 128] 28 -588949/22061796480 + (4499*α)/22061796480

[14 -70 352] 28 -588949/4412359296 + (4499*α)/4412359296

[8 -42 224] 28 -588949/22061796480 + (4499*α)/22061796480

[8 -106 1408] 28 588949/7353932160 - (4499*α)/7353932160

[16 -113 800] 31 -3110612873/45182559191040 + (7851103*α)/45182559191040

[8 -113 1600] 31 -3110612873/45182559191040 + (7851103*α)/45182559191040

[14 -47 160] 31 2404836247/45182559191040 + (7851103*α)/45182559191040

[20 -101 512] 39 11343291269/30121706127360 + (23373341*α)/30121706127360

[10 -91 832] 39 1846810903/10040568709120 - (47176353*α)/10040568709120

[10 -101 1024] 39 1846810903/10040568709120 - (47176353*α)/10040568709120

[8 -27 96] 39 8116849349/30121706127360 + (62061341*α)/30121706127360

[24 -73 224] 47 48571056421/45182559191040 - (117852611*α)/45182559191040

[12 -73 448] 47 -39454137083/45182559191040 + (141142333*α)/45182559191040

[4 9 32] 47 48571056421/45182559191040 - (117852611*α)/45182559191040

[8 -73 672] 47 -39454137083/45182559191040 + (141142333*α)/45182559191040

[16 -55 192] 47 -7215687199/9036511838208 + (125794649*α)/9036511838208

[2 4 32] 48 0

[26 76 224] 48 0

[6 12 32] 48 0

[14 36 96] 48 0

[2 3 32] 55 -926467623211/90365118382080 + (4875945581*α)/90365118382080

[14 -29 64] 55 100165449553/18073023676416 - (656084663*α)/18073023676416

[14 -99 704] 55 100165449553/18073023676416 - (656084663*α)/18073023676416

[8 -35 160] 55 -459988453483/90365118382080 + (4261859693*α)/90365118382080

[2 2 32] 60 50565571/7353932160 - (19847*α)/2451310720

[30 -210 1472] 60 -17725811/2451310720 + (404143*α)/7353932160

[16 -50 160] 60 21009787/1470786432 - (42399*α)/490262144

[16 -178 1984] 60 1305931/7353932160 - (172301*α)/7353932160

[10 -30 96] 60 69597313/2451310720 - (1099669*α)/7353932160

[10 -50 256] 60 21009787/1470786432 - (42399*α)/490262144

[8 -50 320] 60 -156920437/7353932160 + (867827*α)/7353932160

[8 -114 1632] 60 -17725811/2451310720 + (404143*α)/7353932160

[2 1 32] 63 78755323597/30121706127360 + (13459813*α)/30121706127360

[16 -225 3168] 63 -391048548467/30121706127360 + (2896111717*α)/30121706127360

[4 33 288] 63 -391048548467/30121706127360 + (2896111717*α)/30121706127360

[12 -159 2112] 63 4337925739/1255071088640 - (2254189*α)/1255071088640

[8 -97 1184] 63 574583912269/30121706127360 - (4080897179*α)/30121706127360

[2 0 32] 64 11843/11490519 - (1105*α)/11490519

[2 8 64] 64 -11843/22981038 + (1105*α)/22981038

[2 16 160] 64 0

[4 8 32] 64 -11843/22981038 + (1105*α)/22981038

[20 56 160] 64 11843/22981038 - (1105*α)/22981038

[10 -24 64] 64 11843/22981038 - (1105*α)/22981038

[10 -64 416] 64 -11843/11490519 + (1105*α)/11490519

[10 -144 2080] 64 0

[36 -469 6112] 71 65577679011/2008113741824 - (234626741*α)/2008113741824

[18 -181 1824] 71 -153068747891/30121706127360 + (1343989861*α)/30121706127360

[18 -235 3072] 71 7158418351/10040568709120 - (749020041*α)/10040568709120

[12 -85 608] 71 -153068747891/30121706127360 + (1343989861*α)/30121706127360

[120 277 640] 71 65577679011/2008113741824 - (234626741*α)/2008113741824

[10 -43 192] 71 37975584111/10040568709120 - (1236309641*α)/10040568709120

[10 -53 288] 71 7158418351/10040568709120 - (749020041*α)/10040568709120

[40 -441 4864] 79 105299013547/45182559191040 + (1961999923*α)/45182559191040

[20 -121 736] 79 3208597485067/45182559191040 - (18808588877*α)/45182559191040

[190 441 1024] 79 105299013547/45182559191040 + (1961999923*α)/45182559191040

[10 -71 512] 79 3208597485067/45182559191040 - (18808588877*α)/45182559191040

[10 -121 1472] 79 -916607799601/9036511838208 + (3983530967*α)/9036511838208

[44 -397 3584] 87 455666578783/30121706127360 + (531313549*α)/10040568709120

[22 -45 96] 87 -177733280335/2008113741824 + (4665589435*α)/6024341225472

[22 -243 2688] 87 182523348319/30121706127360 - (3118717043*α)/10040568709120

[16 -115 832] 87 -177733280335/2008113741824 + (4665589435*α)/6024341225472

[12 -51 224] 87 1027434151861/10040568709120 - (25991934553*α)/30121706127360

[134 307 704] 87 455666578783/30121706127360 + (531313549*α)/10040568709120

[46 -138 416] 92 3788862467/22061796480 - (5243797*α)/22061796480

[46 -230 1152] 92 -2993781401/22061796480 + (21570991*α)/22061796480

[4 6 32] 92 -2993781401/22061796480 + (21570991*α)/22061796480

[24 -218 1984] 92 -132513511/7353932160 - (2721199*α)/7353932160

[26 70 192] 92 1277020667/4412359296 - (6995677*α)/4412359296

[162 374 864] 92 3788862467/22061796480 - (5243797*α)/22061796480

[6 26 128] 92 -2993781401/22061796480 + (21570991*α)/22061796480

[26 -86 288] 92 -5590022269/22061796480 + (51305579*α)/22061796480

[12 -26 64] 92 -132513511/7353932160 - (2721199*α)/7353932160

[12 -38 128] 92 -132513511/7353932160 - (2721199*α)/7353932160

[12 -122 1248] 92 1277020667/4412359296 - (6995677*α)/4412359296

[12 -134 1504] 92 -2993781401/22061796480 + (21570991*α)/22061796480

[48 -337 2368] 95 -18798165596483/90365118382080 + (122941982293*α)/90365118382080

[24 -337 4736] 95 -5846441379779/90365118382080 + (42628679509*α)/90365118382080

[4 17 96] 95 12405056113021/90365118382080 - (60224491691*α)/90365118382080

[16 -81 416] 95 12405056113021/90365118382080 - (60224491691*α)/90365118382080

[6 49 416] 95 -5846441379779/90365118382080 + (42628679509*α)/90365118382080

[12 -145 1760] 95 20860858934461/90365118382080 - (110454095531*α)/90365118382080

[60 145 352] 95 3472410520189/90365118382080 + (2793847381*α)/90365118382080

[10 15 32] 95 -18798165596483/90365118382080 + (122941982293*α)/90365118382080

[52 -261 1312] 103 -12381481910629/90365118382080 + (71599022339*α)/90365118382080

[4 5 32] 103 -12381481910629/90365118382080 + (71599022339*α)/90365118382080

[26 -261 2624] 103 10757550985883/90365118382080 - (78420990973*α)/90365118382080

[14 -59 256] 103 -33219366871717/90365118382080 + (278887798787*α)/90365118382080

[14 -101 736] 103 10757550985883/90365118382080 - (78420990973*α)/90365118382080

[56 -169 512] 111 3350404878557/6024341225472 - (7695433675*α)/6024341225472

[28 -169 1024] 111 692034012445/6024341225472 - (12660540107*α)/6024341225472

[120 297 736] 111 -18141136646959/30121706127360 + (64380899849*α)/30121706127360

[6 9 32] 111 3350404878557/6024341225472 - (7695433675*α)/6024341225472

[14 -169 2048] 111 -3196176376229/10040568709120 + (34180961539*α)/10040568709120

[14 -183 2400] 111 9620528423323/10040568709120 - (50133702653*α)/10040568709120

[12 -87 640] 111 692034012445/6024341225472 - (12660540107*α)/6024341225472

[10 23 64] 111 -18141136646959/30121706127360 + (64380899849*α)/30121706127360

[2 4 64] 112 -37692736/172357785 + (287936*α)/172357785

[58 172 512] 112 37692736/172357785 - (287936*α)/172357785

[4 4 32] 112 -37692736/172357785 + (287936*α)/172357785

[28 -84 256] 112 0

[28 -140 704] 112 75385472/172357785 - (575872*α)/172357785

[28 -196 1376] 112 -37692736/172357785 + (287936*α)/172357785

[14 -28 64] 112 -37692736/172357785 + (287936*α)/172357785

[14 -84 512] 112 37692736/172357785 - (287936*α)/172357785

[8 12 32] 112 37692736/172357785 - (287936*α)/172357785

[16 -84 448] 112 0

[16 -148 1376] 112 37692736/172357785 - (287936*α)/172357785

[16 -212 2816] 112 -75385472/172357785 + (575872*α)/172357785

[2 3 64] 119 -8749558828031/45182559191040 + (117016329241*α)/45182559191040

[30 -61 128] 119 4375620970753/45182559191040 - (126624306023*α)/45182559191040

[30 -451 6784] 119 -8749558828031/45182559191040 + (117016329241*α)/45182559191040

[20 -61 192] 119 48521112949729/45182559191040 - (230608329959*α)/45182559191040

[90 221 544] 119 -181672525363/9036511838208 - (3462582907*α)/9036511838208

[16 -67 288] 119 26941661617441/45182559191040 - (92456589671*α)/45182559191040

[8 67 576] 119 4375620970753/45182559191040 - (126624306023*α)/45182559191040

[12 -61 320] 119 48521112949729/45182559191040 - (230608329959*α)/45182559191040

[24 61 160] 119 -92130813635231/45182559191040 + (416127359641*α)/45182559191040

[12 -125 1312] 119 -181672525363/9036511838208 - (3462582907*α)/9036511838208

[2 2 64] 124 2404836247/11030898240 + (7851103*α)/11030898240

[62 -434 3040] 124 -2007523049/2206179648 + (7851103*α)/2206179648

[4 2 32] 124 2404836247/11030898240 + (7851103*α)/11030898240

[32 -226 1600] 124 1272129833/3676966080 - (7851103*α)/3676966080

[16 -98 608] 124 -8626061993/11030898240 + (7851103*α)/11030898240

[16 -226 3200] 124 1272129833/3676966080 - (7851103*α)/3676966080

[8 34 160] 124 2404836247/11030898240 + (7851103*α)/11030898240

[28 -94 320] 124 1272129833/3676966080 - (7851103*α)/3676966080

[10 14 32] 124 -2007523049/2206179648 + (7851103*α)/2206179648

[14 -46 160] 124 198656599/2206179648 + (7851103*α)/2206179648

[14 -130 1216] 124 -8626061993/11030898240 + (7851103*α)/11030898240

[14 -158 1792] 124 2404836247/11030898240 + (7851103*α)/11030898240

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[8 33 192] 447 94779062856841789/30121706127360 - (557947195619819*α)/30121706127360

[38 -193 992] 447 94779062856841789/30121706127360 - (557947195619819*α)/30121706127360

[38 -383 3872] 447 27484352727616025/6024341225472 - (182144170843951*α)/6024341225472

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[8 8 64] 448 154389446656/172357785 - (1179385856*α)/172357785

[56 -168 512] 448 0

[56 -280 1408] 448 -308778893312/172357785 + (2358771712*α)/172357785

[56 -392 2752] 448 154389446656/172357785 - (1179385856*α)/172357785

[58 -120 256] 448 63169952128/57452595 - (314388608*α)/57452595

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[58 -816 11488] 448 3644377720/11490519 + (47438680*α)/11490519

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[14 56 256] 448 -27130613576/19150865 + (25731736*α)/19150865

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[28 -56 128] 448 154389446656/172357785 - (1179385856*α)/172357785

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[32 -104 352] 448 27130613576/19150865 - (25731736*α)/19150865

[32 -168 896] 448 0

[32 -232 1696] 448 63169952128/57452595 - (314388608*α)/57452595

[32 -296 2752] 448 -154389446656/172357785 + (1179385856*α)/172357785

[32 -360 4064] 448 -27130613576/19150865 + (25731736*α)/19150865

[32 -424 5632] 448 308778893312/172357785 - (2358771712*α)/172357785

[22 -72 256] 448 27130613576/19150865 - (25731736*α)/19150865

[22 -160 1184] 448 -144561792856/57452595 + (391583816*α)/57452595

[22 -336 5152] 448 -3644377720/11490519 - (47438680*α)/11490519

[228 -2965 38560] 455 607880443255517/705977487360 - (21772025261639*α)/1411954974720

[114 -1141 11424] 455 -115824479333611/282390994944 + (2659540253381*α)/282390994944

[114 -1483 19296] 455 -4569049655964839/1411954974720 + (32593244600569*α)/1411954974720

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[58 -235 960] 455 1545277454210701/1411954974720 - (27671455204571*α)/1411954974720

[58 -757 9888] 455 -217170331174307/1411954974720 - (5968830785603*α)/1411954974720

[48 -341 2432] 455 748519924645381/352988743680 + (1722755377021*α)/1411954974720

[38 -267 1888] 455 -1146585353916359/1411954974720 + (5609141885389*α)/1411954974720

[38 -533 7488] 455 748519924645381/352988743680 + (1722755377021*α)/1411954974720

[40 -85 192] 455 -1146585353916359/1411954974720 + (5609141885389*α)/1411954974720

[62 -203 672] 455 1469616891138347/282390994944 - (7551594223327*α)/282390994944

[14 21 64] 455 -4569049655964839/1411954974720 + (32593244600569*α)/1411954974720

[30 -395 5216] 455 -2053941264610493/1411954974720 + (29052544795453*α)/1411954974720

[28 -427 6528] 455 607880443255517/705977487360 - (21772025261639*α)/1411954974720

[18 43 128] 455 -217170331174307/1411954974720 - (5968830785603*α)/1411954974720

[24 -341 4864] 455 -299929584698429/88247185920 + (16103110632469*α)/1411954974720

[20 85 384] 455 -917676832822351/282390994944 + (2913213132221*α)/282390994944

[24 -299 3744] 455 -917676832822351/282390994944 + (2913213132221*α)/282390994944

[232 -2553 28096] 463 20356321895531279/45182559191040 - (304452791262409*α)/45182559191040

[116 -697 4192] 463 -40901743795036561/45182559191040 + (446004751883831*α)/45182559191040

[1054 2457 5728] 463 -95519046996990097/45182559191040 + (747812009888567*α)/45182559191040

[58 -697 8384] 463 140996834710771631/45182559191040 - (1112175335413321*α)/45182559191040

[58 -871 13088] 463 -95519046996990097/45182559191040 + (747812009888567*α)/45182559191040

[16 7 32] 463 20356321895531279/45182559191040 - (304452791262409*α)/45182559191040

[236 -2125 19136] 471 34561182846011003/30121706127360 + (265814248081187*α)/30121706127360

[118 -237 480] 471 50433458348889083/30121706127360 - (754382201011933*α)/30121706127360

[118 -1299 14304] 471 -58932215255879173/30121706127360 + (161034300653603*α)/30121706127360

[80 -563 3968] 471 36095789014201787/30121706127360 + (131654036859683*α)/30121706127360

[60 -243 992] 471 24849630461159803/30121706127360 - (5576917911773*α)/30121706127360

[74 211 608] 471 91666569480746299/30121706127360 - (296220707248349*α)/30121706127360

[10 13 64] 471 -58932215255879173/30121706127360 + (161034300653603*α)/30121706127360

[10 83 736] 471 1796095772242811/30121706127360 - (578043936504541*α)/30121706127360

[40 -563 7936] 471 1796095772242811/30121706127360 - (578043936504541*α)/30121706127360

[12 51 256] 471 -76910337058748869/30121706127360 + (437524223368739*α)/30121706127360

[30 -333 3712] 471 -76910337058748869/30121706127360 + (437524223368739*α)/30121706127360

[24 -51 128] 471 91666569480746299/30121706127360 - (296220707248349*α)/30121706127360

[50 -173 608] 471 -100299431569372997/30121706127360 + (974229573527587*α)/30121706127360

[26 -371 5312] 471 36095789014201787/30121706127360 + (131654036859683*α)/30121706127360

[26 -397 6080] 471 34561182846011003/30121706127360 + (265814248081187*α)/30121706127360

[238 -714 2144] 476 31318965701669/11030898240 - (355313178499*α)/11030898240

[238 -1190 5952] 476 8013368283245/2206179648 - (67219444987*α)/2206179648

[4 6 128] 476 4374498895103/3676966080 - (35802784153*α)/3676966080

[120 -1082 9760] 476 -4374947725363/2206179648 + (72131392901*α)/2206179648

[90 262 768] 476 -92130813635231/11030898240 + (416127359641*α)/11030898240

[738 1718 4000] 476 -35870043001247/2206179648 + (157433083801*α)/2206179648

[6 26 192] 476 48521112949729/11030898240 - (230608329959*α)/11030898240

[90 -278 864] 476 44887662442469/11030898240 - (299859988099*α)/11030898240

[60 -122 256] 476 -7522574586721/3676966080 + (34021522151*α)/3676966080

[60 -422 2976] 476 4375620970753/11030898240 - (126624306023*α)/11030898240

[60 -602 6048] 476 -31315599474719/11030898240 + (82848612889*α)/11030898240

[60 -902 13568] 476 4374498895103/3676966080 - (35802784153*α)/3676966080

[10 22 96] 476 44887662442469/11030898240 - (299859988099*α)/11030898240

[210 518 1280] 476 -50337838203359/11030898240 + (195982500889*α)/11030898240

[10 42 224] 476 52524162587141/11030898240 - (293010544771*α)/11030898240

[62 -198 640] 476 27948712791629/2206179648 - (132809720827*α)/2206179648

[40 -122 384] 476 14839354437439/3676966080 - (56068705049*α)/3676966080

[40 -442 4896] 476 27948712791629/2206179648 - (132809720827*α)/2206179648

[12 26 96] 476 48521112949729/11030898240 - (230608329959*α)/11030898240

[180 442 1088] 476 -15568129232033/3676966080 + (88411386343*α)/3676966080

[34 -102 320] 476 -42701338058687/11030898240 + (202831944217*α)/11030898240

[34 -170 864] 476 52524162587141/11030898240 - (293010544771*α)/11030898240

[30 -122 512] 476 26941661617441/11030898240 - (92456589671*α)/11030898240

[30 -182 1120] 476 -30622614341371/11030898240 + (341441010941*α)/11030898240

[30 -362 4384] 476 89576226793829/11030898240 - (530618381059*α)/11030898240

[30 -422 5952] 476 4375620970753/11030898240 - (126624306023*α)/11030898240

[16 6 32] 476 8013368283245/2206179648 - (67219444987*α)/2206179648

[32 -134 576] 476 -11897634519649/3676966080 + (115235067239*α)/3676966080

[32 -390 4768] 476 26941661617441/11030898240 - (92456589671*α)/11030898240

[16 134 1152] 476 -7522574586721/3676966080 + (34021522151*α)/3676966080

[18 26 64] 476 -4374947725363/2206179648 + (72131392901*α)/2206179648

[30 -218 1600] 476 -31315599474719/11030898240 + (82848612889*α)/11030898240

[30 -278 2592] 476 -30622614341371/11030898240 + (341441010941*α)/11030898240

[30 -458 7008] 476 31318965701669/11030898240 - (355313178499*α)/11030898240

[24 -122 640] 476 14839354437439/3676966080 - (56068705049*α)/3676966080

[24 -314 4128] 476 -42701338058687/11030898240 + (202831944217*α)/11030898240

[48 122 320] 476 -545712473803/1225655360 + (5009922253*α)/1225655360

[248 570 1312] 476 -92130813635231/11030898240 + (416127359641*α)/11030898240

[24 -58 160] 476 -50337838203359/11030898240 + (195982500889*α)/11030898240

[24 -250 2624] 476 -15568129232033/3676966080 + (88411386343*α)/3676966080

[240 -1681 11776] 479 6317420938400971/3765213265920 - (64544977201061*α)/3765213265920

[120 -1681 23552] 479 13898814429642683/3765213265920 - (49402669697413*α)/3765213265920

[4 17 192] 479 323280855333067/3765213265920 + (35794165875163*α)/3765213265920

[80 -401 2016] 479 5889170413883337/1255071088640 - (46593449338647*α)/1255071088640

[6 49 480] 479 22118100445562779/3765213265920 - (156540651468389*α)/3765213265920

[60 -721 8672] 479 -9484157103070607/1255071088640 + (49040150647017*α)/1255071088640

[8 17 96] 479 5889170413883337/1255071088640 - (46593449338647*α)/1255071088640

[48 -145 448] 479 -7416512057432369/753042653184 + (45095755831327*α)/753042653184

[10 81 704] 479 1311690109156951/753042653184 - (3152636169185*α)/753042653184

[40 -401 4032] 479 -13876509980195101/3765213265920 + (122863649799131*α)/3765213265920

[54 -175 576] 479 -1235179043250157/3765213265920 + (21554477300987*α)/3765213265920

[12 17 64] 479 323280855333067/3765213265920 + (35794165875163*α)/3765213265920

[42 -593 8384] 479 1311690109156951/753042653184 - (3152636169185*α)/753042653184

[36 -401 4480] 479 -1235179043250157/3765213265920 + (21554477300987*α)/3765213265920

[178 433 1056] 479 20378348428341451/3765213265920 - (126341582924261*α)/3765213265920

[30 -271 2464] 479 -13876509980195101/3765213265920 + (122863649799131*α)/3765213265920

[28 -145 768] 479 -7416512057432369/753042653184 + (45095755831327*α)/753042653184

[56 145 384] 479 1744638430362191/753042653184 - (12587388415297*α)/753042653184

[24 -145 896] 479 1744638430362191/753042653184 - (12587388415297*α)/753042653184

[20 81 352] 479 1275668711621815/753042653184 - (12996936348353*α)/753042653184

[28 -401 5760] 479 22118100445562779/3765213265920 - (156540651468389*α)/3765213265920

[168 401 960] 479 20378348428341451/3765213265920 - (126341582924261*α)/3765213265920

[24 -367 5632] 479 6317420938400971/3765213265920 - (64544977201061*α)/3765213265920

[60 -209 736] 479 1275668711621815/753042653184 - (12996936348353*α)/753042653184

[244 -1221 6112] 487 4353138436177931/10040568709120 - (98972370890061*α)/10040568709120

[4 5 128] 487 -42221909790075167/30121706127360 + (349281114131737*α)/30121706127360

[122 -1221 12224] 487 -89540421593105759/30121706127360 + (854485893130009*α)/30121706127360

[62 -933 14048] 487 -42221909790075167/30121706127360 + (349281114131737*α)/30121706127360

[16 5 32] 487 4353138436177931/10040568709120 - (98972370890061*α)/10040568709120

[248 -745 2240] 495 -235335701703900941/30121706127360 + (970155420986011*α)/30121706127360

[124 -745 4480] 495 -12551000485988237/30121706127360 + (48541227798427*α)/30121706127360

[504 1257 3136] 495 87283274024665459/30121706127360 - (484851189900389*α)/30121706127360

[6 9 96] 495 821882166692821/1255071088640 - (33181608415891*α)/1255071088640

[62 -311 1568] 495 2277632101644887/6024341225472 - (34698711880417*α)/6024341225472

[52 -681 8928] 495 -69238770093004109/30121706127360 + (1101507268400539*α)/30121706127360

[42 -87 192] 495 -440358537201583/251014217728 + (1851884190793*α)/251014217728

[42 -297 2112] 495 -440358537201583/251014217728 + (1851884190793*α)/251014217728

[36 -471 6176] 495 -10481692236433613/30121706127360 - (89813938488677*α)/30121706127360

[56 151 416] 495 80931484690856371/30121706127360 - (548716253571941*α)/30121706127360

[16 23 64] 495 87283274024665459/30121706127360 - (484851189900389*α)/30121706127360

[28 -87 288] 495 235632291498186739/30121706127360 - (1721869362432869*α)/30121706127360

[142 343 832] 495 -111557308436893709/30121706127360 + (913129297424539*α)/30121706127360

[18 9 32] 495 -235335701703900941/30121706127360 + (970155420986011*α)/30121706127360

[26 -265 2720] 495 80931484690856371/30121706127360 - (548716253571941*α)/30121706127360

[26 -343 4544] 495 -10481692236433613/30121706127360 - (89813938488677*α)/30121706127360

[28 -151 832] 495 -69238770093004109/30121706127360 + (1101507268400539*α)/30121706127360

[24 -105 480] 495 5427470975089813/1255071088640 + (8309140768877*α)/1255071088640

[2 4 256] 496 45169704064/172357785 - (1004941184*α)/172357785

[250 748 2240] 496 -45169704064/172357785 + (1004941184*α)/172357785

[4 4 128] 496 -2048

[124 -372 1120] 496 41467662784/34471557 - (543283520*α)/34471557

[124 -620 3104] 496 -297677722048/172357785 + (4726299968*α)/172357785

[124 -868 6080] 496 443328151808/172357785 - (2009882368*α)/172357785

[62 -124 256] 496 45169704064/172357785 - (1004941184*α)/172357785

[62 -372 2240] 496 -45169704064/172357785 + (1004941184*α)/172357785

[8 4 64] 496 -2048

[64 -196 608] 496 29130085952/34471557 + (543283520*α)/34471557

[64 -452 3200] 496 -443328151808/172357785 + (2009882368*α)/172357785

[64 -708 7840] 496 650666465728/172357785 - (4726299968*α)/172357785

[10 12 64] 496 -297677722048/172357785 + (4726299968*α)/172357785

[50 -252 1280] 496 650666465728/172357785 - (4726299968*α)/172357785

[50 -452 4096] 496 -41467662784/34471557 + (543283520*α)/34471557

[50 -652 8512] 496 -29130085952/34471557 - (543283520*α)/34471557

[14 20 64] 496 41467662784/34471557 - (543283520*α)/34471557

[38 -196 1024] 496 29130085952/34471557 + (543283520*α)/34471557

[38 -348 3200] 496 297677722048/172357785 - (4726299968*α)/172357785

[38 -500 6592] 496 -650666465728/172357785 + (4726299968*α)/172357785

[16 4 32] 496 45169704064/172357785 - (1004941184*α)/172357785

[32 -68 160] 496 -41467662784/34471557 + (543283520*α)/34471557

[32 -196 1216] 496 2048

[32 -324 3296] 496 297677722048/172357785 - (4726299968*α)/172357785

[32 -452 6400] 496 -443328151808/172357785 + (2009882368*α)/172357785

[16 68 320] 496 0

[56 -188 640] 496 -90339408128/172357785 + (2009882368*α)/172357785

[20 28 64] 496 443328151808/172357785 - (2009882368*α)/172357785

[28 -92 320] 496 90339408128/172357785 - (2009882368*α)/172357785

[28 -148 800] 496 -29130085952/34471557 - (543283520*α)/34471557

[28 -260 2432] 496 2048

[28 -316 3584] 496 0

[28 -372 4960] 496 -650666465728/172357785 + (4726299968*α)/172357785

[28 -428 6560] 496 -45169704064/172357785 + (1004941184*α)/172357785

A nonlift newform in S14(K(16))+

A nonlift newform in S₁₄(K(16))⁺