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

A nonlift newform in S₁₄(K(16))⁺

(Filename: eigs/eig-plus-14-16-7.html)

FORMULA FOR THE EIGENFORM f
with 3¹⁴⁻³λ₃ = 498216 + 2112*α,
where throughout this wepage, α is taken to have minimal polynomial -8689 + 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	581807187586844417069151404909389500530342647613423247304656754538606010262445721208160761080133516750711909876878197375357802422015240194645956424071522199619130278407848676201210383007688622381796155284097456959201081931966032436668804810605720670463800542009519452481044411652763088175213885626695900506772893174133816193301077921079854967288055923928534362996174769764103488614932170567846663914713557463949954672229695103/16752577821456065820759445554670135779828668859293777522009033036256211959315927279301472389804482973489754217828216505852709240355277845250340977010442447333167235877583928369939119275904074249705286557904130994056631855224316462287726416921531250356201301120567580703108328315697660573288135570738697277745601197137830161639402055287935504973033237509727140626471694695150850323752233839099904000000 - (6241576367692913908544803704313934161503788569128925335188511386999373142588152152476545560269786822937019903670429601358659626248018032092284666775891401815805660635359424630428635986709360935848577705605704620341276917493282190236629645680992937618361453109898507584763343593537652710781483656066386156954881904972644221530058841286963319269102269348899475384335520210605174138543251897708506608784987479708940724267791209*α)/16752577821456065820759445554670135779828668859293777522009033036256211959315927279301472389804482973489754217828216505852709240355277845250340977010442447333167235877583928369939119275904074249705286557904130994056631855224316462287726416921531250356201301120567580703108328315697660573288135570738697277745601197137830161639402055287935504973033237509727140626471694695150850323752233839099904000000
b₂	-1757738805390539029905254706137725106621451897816218026304268656510273657679136795589595232725827117726325200738113945052288694162730152056501675531470696191865239123643122380649397597965040068860444302211169653726641237218178080949220424856791480207504243023657801711877198146191453773612802089444311686624323301508835807140694841701110785629233840967496653867080481697564562848710462458307337597964583334179389582577999351211/41881444553640164551898613886675339449571672148234443805022582590640529898289818198253680974511207433724385544570541264631773100888194613125852442526106118332918089693959820924847798189760185624263216394760327485141579638060791155719316042303828125890503252801418951757770820789244151433220338926846743194364002992844575404098505138219838762432583093774317851566179236737877125809380584597749760000000 + (18856867432825886020155544177639871690460131125325245798633077874257162467385124055788103471519603964107255126057068335434194345344978108588785086592675205317016416812046515890682574640548172754798899090999599010608732090735788104001323382174998900464059944862788659085420946811630610017702264764080837373289838031238775240390992591248930885942061896478707670077837185024754527707327931623228999805272882904853667404436080733*α)/41881444553640164551898613886675339449571672148234443805022582590640529898289818198253680974511207433724385544570541264631773100888194613125852442526106118332918089693959820924847798189760185624263216394760327485141579638060791155719316042303828125890503252801418951757770820789244151433220338926846743194364002992844575404098505138219838762432583093774317851566179236737877125809380584597749760000000
b₃	235443732801428872543657550937393507608715777692513839651372856039142972002765476438273158863439890983096671590751478655602152953377992034884694430696020143093556197206830036254816931236639341426696850882935934579142169118652972076865420529719418968091079252457916507910058446466138871342040783196671310167716665034307416465589750769630297404444200170130229727020632251586188244799397071653389516501865676995527217710268081613/4188144455364016455189861388667533944957167214823444380502258259064052989828981819825368097451120743372438554457054126463177310088819461312585244252610611833291808969395982092484779818976018562426321639476032748514157963806079115571931604230382812589050325280141895175777082078924415143322033892684674319436400299284457540409850513821983876243258309377431785156617923673787712580938058459774976000000 - (2525819674603743643169653051376120139837825061382308998032560309911311194330411240537981271672324298979767229636755182049193511817151673075137950393537437179256910179727984465929468570527530158600383214039247194494052183178246884108162458054951292538448693605691037879220775674806017030132319432191228489754625206843192945447270336898935856674426553138875901100234685803802489105213306347571910099196030354864924581443340139*α)/4188144455364016455189861388667533944957167214823444380502258259064052989828981819825368097451120743372438554457054126463177310088819461312585244252610611833291808969395982092484779818976018562426321639476032748514157963806079115571931604230382812589050325280141895175777082078924415143322033892684674319436400299284457540409850513821983876243258309377431785156617923673787712580938058459774976000000
b₄	304124866022031308748336805589481904747970164728002605990861483231912861406876203088064849225773152587563699435593720222459758663526023828885154520413788790142634989366053767147349507501631077051596995311057873404654088788603903362127877924654258157631067276311047843167440781970957471356388205551698968795547972066463092458744843504082873235139093006222623128387802842213939341460823065900186954086158053001338175011066400579/5384757156896592585244107499715400786373500704772999917788617761653782415494405196918330411008583812907420998587641019738370827257053593116181028324785072357089468674937691261766145481540595294548127822183470676661060239179244577163912062581920759043064703931611008083141962672902819469985472147737438410703943241937159694812664946342550698027046397770983723772794473294869916175491789448282112000000 - (3262624836040763724924107053513444451962427929768895080909050161180250002582957672273277810651942193108392651400644363234297414360293515886549158017562254964066165914170248107926833834754023127132597792946534916024676860615272832905655277290274060277936327095443574047694784390810724677658132423616572093043648466235950740652473116807737938927103494298383529048037355184891336305378234514292688551658753359516677666630655237*α)/5384757156896592585244107499715400786373500704772999917788617761653782415494405196918330411008583812907420998587641019738370827257053593116181028324785072357089468674937691261766145481540595294548127822183470676661060239179244577163912062581920759043064703931611008083141962672902819469985472147737438410703943241937159694812664946342550698027046397770983723772794473294869916175491789448282112000000
b₅	662233307316880711271544227477159259999259196908493582273488072485742120751322209058383857512315869809950717576708196962674512221124517095133984072691039504558019216723952784881994338734903678669685865151635248920472759242166617770895650916727284024816557296730151455919569800702416687378533000449387934832909481020436425380024926040776520498801064424686612120516247135081488495234499266362084251426952446266463158907247125051/9046392023586275543210100599521873321107481184018639861884877839578354458030600730822795090494420805684467277627236913160462989791850036435184127585638921559910307373895321319767124408988200094840854741268230736790581201821130889635372265137626875192348702605106493579678497290476736709575593208198896529982624646454428287285277109855485172685437948255252655938294715135381459174826206273113948160000 - (7104380723646865623519522188399507654926126319158746804510318712433976419911508853363614676585663776725330616494081110600838672860459958843311369148790770229040451534646680204322951351313722413747248446576598723570192454856154146408890391828606381811651371620996414674383269025696366378932116451930421209981564417387365865584694196179809986247962493549176416018928887726626964323260215837210349944224007402623847146027729229*α)/9046392023586275543210100599521873321107481184018639861884877839578354458030600730822795090494420805684467277627236913160462989791850036435184127585638921559910307373895321319767124408988200094840854741268230736790581201821130889635372265137626875192348702605106493579678497290476736709575593208198896529982624646454428287285277109855485172685437948255252655938294715135381459174826206273113948160000
b₆	106012621891122487734893789221820234978437621609967445440960577529465485066234084551402190079829896013020295895486126596764456098961565982999706667911076321542948710418504582943112295972370065557716433078023789882626044962481428043437298428332205794357236467517794821107036025919167710447555769790853415035355417265503789258109195785237090780949210357668783586834703208891821866939902535316557294588010788033803883913170111318737/2261598005896568885802525149880468330276870296004659965471219459894588614507650182705698772623605201421116819406809228290115747447962509108796031896409730389977576843473830329941781102247050023710213685317057684197645300455282722408843066284406718798087175651276623394919624322619184177393898302049724132495656161613607071821319277463871293171359487063813163984573678783845364793706551568278487040000000 - (1137294091251202048520304995357449303330855435458284552879208084591676538400554533784238183051459200526113987875243889781317659791240101377561685439620140353081659194072865072010072544536845414980257503451161903100486298155492507318216002350305954196132018229791712836975714219162541860981136934370213845588139169947844811718108301290407733653800953549230206548995669067724691658829466412463604552671010257847475785619397427911*α)/2261598005896568885802525149880468330276870296004659965471219459894588614507650182705698772623605201421116819406809228290115747447962509108796031896409730389977576843473830329941781102247050023710213685317057684197645300455282722408843066284406718798087175651276623394919624322619184177393898302049724132495656161613607071821319277463871293171359487063813163984573678783845364793706551568278487040000000
b₇	66284458296035075067568466787450378980986256143322293588998130356051232175388071954552364307957625663120372517884094403364598553744538154166302154577202563827685366956769128085344842380175102657637123729941055187089241721824256462336599737548688915732497726310437358208134419975349605015225573321419016475870305445718486620266831224340348002702118312821856411061384827339935217306215871203272570653650940411152098611705848902237/484628144120693332671969674974386070773615063429569992600975598548840417394496467722649736990772543161667889872887691776453374453134823380456292549230656512138052180744392213558953093338653576509331503996512360899495421526132011944752085632372868313875823353844990727482776640561253752298692493296369456963354891774344372533139845170829562822434175799388535139551502596538292455794261050345390080000000 - (711093843292413694033893947374320104277343812852784081593181243623385292348784554754528722528110881052438090828238533410383196375617520267462829904611390677921086587335823660149528927580600510506088633413231704243892703303260761429211782849896512048645756658945005969163702647192921952291611238389080043933727064703667434470163310252191075466834921141860650041003658862072724212553898227978882151911898829421841609888703416411*α)/484628144120693332671969674974386070773615063429569992600975598548840417394496467722649736990772543161667889872887691776453374453134823380456292549230656512138052180744392213558953093338653576509331503996512360899495421526132011944752085632372868313875823353844990727482776640561253752298692493296369456963354891774344372533139845170829562822434175799388535139551502596538292455794261050345390080000000
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c_1,39	-155586070429075436487935664692271162452412571911919642015408934564165897048659374625224892308599238316513871303154394317608225137420169092861612738522774687600555511869857098071134906306633773069761327804456602757740414520683825843179595407039512582486799629374826290461231980212251038765415607071768767691364153/126360811834461351919179211874822478307449284893386989881592210000880353254504069976085939634843070045745943046855807841023545789467717520096293605960734519668133827299326659830021640353473088043612344596358243286158444089064265668379308250894682384731617195597561725521767344656501395475082866829354385426836880988569600000000 + (1669113645135707521625495639564012403357195458092124848566104784597253579426392996119914297050655472682104897126350355412889803895003060983303577070775914003046892359951342483908697021580930815280452704229305404739256837471106202427191552488680021883144929462203272782432652065883082313145442879704503554044959*α)/126360811834461351919179211874822478307449284893386989881592210000880353254504069976085939634843070045745943046855807841023545789467717520096293605960734519668133827299326659830021640353473088043612344596358243286158444089064265668379308250894682384731617195597561725521767344656501395475082866829354385426836880988569600000000
c_1,40	-186262918720141714602340139205869292679192961910983296360432421551327698863261730228446258301097902205491946923726171227750704086196802006982669599250200320719551743584424471903286185159088857428491223232374784186305214912187128695697353117561555354235691667715833945949016299496494713675034479304614902423271/9189877224324461957758488136350725695087220719519053809570342545518571145782114180078977427988586912417886767044058752074439693779470365097912262251689783248591551076314666169456119298434406403171806879735144966266068661022855684973040600065067809798663068770731761856128534156836465125460572133043955303769954980986880000000 + (1998212058387280763122331751769377935534454697379884429189209723044091436834764740821356974076208618511665931179375035030544597514245153134965925014229840716460288977727495026761579561549646742181646724644126490380491598387801837275937975244300539995137109342743447686440836580397260605783394665140887524033*α)/9189877224324461957758488136350725695087220719519053809570342545518571145782114180078977427988586912417886767044058752074439693779470365097912262251689783248591551076314666169456119298434406403171806879735144966266068661022855684973040600065067809798663068770731761856128534156836465125460572133043955303769954980986880000000
c_1,41	35310227595631342218168432407723775217540294814961185188235983475431812518488357771320579730271408508334667052007442087021600400731928069890463700098969940623222344064128443185981857873523160621233552274737333299786853254504855573724478245692911778331444114986723508719136619123562581903623681511329614603765379/16174183914811053045654939119977277223353508466353534704843802880112685216576520956939000273259912965855480709997543403651013861051867842572325581562974018517521129894313812458242769965244555269582380108333855140628280843400226005552551456114519345245647001036487900866786220116032178620810606954157361334635120766536908800000000 - (378805006555280834771492321834939779826250537927061712559807627811297703305108242422436455397948502228889477568956745473048824866250513564954111692653792444263219059883951409776994049527847652190337842938060145188048530603207033040908352304608088529687357854066259806524399385800338471004574029822656533789637*α)/16174183914811053045654939119977277223353508466353534704843802880112685216576520956939000273259912965855480709997543403651013861051867842572325581562974018517521129894313812458242769965244555269582380108333855140628280843400226005552551456114519345245647001036487900866786220116032178620810606954157361334635120766536908800000000
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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 -4528163/110249315139584 - (34243*α)/110249315139584

[8 -89 992] 15 -199385053/110249315139584 - (4551229*α)/110249315139584

[4 -25 160] 15 241636963/110249315139584 + (3473859*α)/110249315139584

[12 -109 992] 23 -3761195871/110249315139584 - (53153087*α)/110249315139584

[6 -13 32] 23 -3761195871/110249315139584 - (53153087*α)/110249315139584

[6 -19 64] 23 -3336083231/110249315139584 - (95227199*α)/110249315139584

[14 -42 128] 28 0

[14 -70 352] 28 -4528163/13458168352 - (34243*α)/13458168352

[8 -42 224] 28 0

[8 -106 1408] 28 4528163/13458168352 + (34243*α)/13458168352

[16 -113 800] 31 5854796225/55124657569792 - (22498943*α)/55124657569792

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[60 -602 6048] 476 -1998109049763/420567761 - (33641870096*α)/420567761

[60 -902 13568] 476 -22207032398951/6729084176 - (78704198183*α)/6729084176

[10 22 96] 476 67400874817783/6729084176 + (617749068327*α)/6729084176

[210 518 1280] 476 -173041388077/420567761 - (9656306544*α)/420567761

[10 42 224] 476 38427365271799/6729084176 - (182393684697*α)/6729084176

[62 -198 640] 476 1637802958547/420567761 + (40352615520*α)/420567761

[40 -122 384] 476 -38427365271799/6729084176 + (182393684697*α)/6729084176

[40 -442 4896] 476 1637802958547/420567761 + (40352615520*α)/420567761

[12 26 96] 476 173041388077/420567761 + (9656306544*α)/420567761

[180 442 1088] 476 -67400874817783/6729084176 - (617749068327*α)/6729084176

[34 -102 320] 476 -1637802958547/420567761 - (40352615520*α)/420567761

[34 -170 864] 476 38427365271799/6729084176 - (182393684697*α)/6729084176

[30 -122 512] 476 0

[30 -182 1120] 476 22207032398951/6729084176 + (78704198183*α)/6729084176

[30 -362 4384] 476 -11523542835417/6729084176 - (129103225049*α)/6729084176

[30 -422 5952] 476 -2108160952148/420567761 - (12987963952*α)/420567761

[16 6 32] 476 1998109049763/420567761 + (33641870096*α)/420567761

[32 -134 576] 476 11523542835417/6729084176 + (129103225049*α)/6729084176

[32 -390 4768] 476 0

[16 134 1152] 476 -87907352429527/6729084176 - (824781542951*α)/6729084176

[18 26 64] 476 2108160952148/420567761 + (12987963952*α)/420567761

[30 -218 1600] 476 -1998109049763/420567761 - (33641870096*α)/420567761

[30 -278 2592] 476 22207032398951/6729084176 + (78704198183*α)/6729084176

[30 -458 7008] 476 87907352429527/6729084176 + (824781542951*α)/6729084176

[24 -122 640] 476 -38427365271799/6729084176 + (182393684697*α)/6729084176

[24 -314 4128] 476 -1637802958547/420567761 - (40352615520*α)/420567761

[48 122 320] 476 -70169537027015/6729084176 - (772249973031*α)/6729084176

[248 570 1312] 476 0

[24 -58 160] 476 -173041388077/420567761 - (9656306544*α)/420567761

[24 -250 2624] 476 -67400874817783/6729084176 - (617749068327*α)/6729084176

[240 -1681 11776] 479 -60851621590031701/13781164392448 - (610391827034989*α)/13781164392448

[120 -1681 23552] 479 -61343269533951429/13781164392448 - (669361870461933*α)/13781164392448

[4 17 192] 479 -88279462234321621/13781164392448 + (255483341594259*α)/13781164392448

[80 -401 2016] 479 -6827337688896229/13781164392448 + (100232602219795*α)/13781164392448

[6 49 480] 479 9261376898611323/13781164392448 + (811754844893075*α)/13781164392448

[60 -721 8672] 479 -55557052148372621/13781164392448 - (1232206718443757*α)/13781164392448

[8 17 96] 479 -6827337688896229/13781164392448 + (100232602219795*α)/13781164392448

[48 -145 448] 479 53442646411908779/13781164392448 - (14600823599213*α)/13781164392448

[10 81 704] 479 -109932171143015821/13781164392448 - (1434595933829741*α)/13781164392448

[40 -401 4032] 479 -48966284335774429/13781164392448 - (1030344303564141*α)/13781164392448

[54 -175 576] 479 133422169258279923/13781164392448 + (828977440751635*α)/13781164392448

[12 17 64] 479 -88279462234321621/13781164392448 + (255483341594259*α)/13781164392448

[42 -593 8384] 479 -109932171143015821/13781164392448 - (1434595933829741*α)/13781164392448

[36 -401 4480] 479 133422169258279923/13781164392448 + (828977440751635*α)/13781164392448

[178 433 1056] 479 -71537025231066645/13781164392448 - (721033339452525*α)/13781164392448

[30 -271 2464] 479 -48966284335774429/13781164392448 - (1030344303564141*α)/13781164392448

[28 -145 768] 479 53442646411908779/13781164392448 - (14600823599213*α)/13781164392448

[56 145 384] 479 42746396177618187/13781164392448 + (440398594630419*α)/13781164392448

[24 -145 896] 479 42746396177618187/13781164392448 + (440398594630419*α)/13781164392448

[20 81 352] 479 -50077559949237197/13781164392448 - (776270679061741*α)/13781164392448

[28 -401 5760] 479 9261376898611323/13781164392448 + (811754844893075*α)/13781164392448

[168 401 960] 479 -71537025231066645/13781164392448 - (721033339452525*α)/13781164392448

[24 -367 5632] 479 -60851621590031701/13781164392448 - (610391827034989*α)/13781164392448

[60 -209 736] 479 -50077559949237197/13781164392448 - (776270679061741*α)/13781164392448

[244 -1221 6112] 487 1488130731106797221/110249315139584 + (15062080632552069*α)/110249315139584

[4 5 128] 487 1027188302616524645/110249315139584 + (3415305434961541*α)/110249315139584

[122 -1221 12224] 487 -141026306613271515/110249315139584 - (3474834555306363*α)/110249315139584

[62 -933 14048] 487 1027188302616524645/110249315139584 + (3415305434961541*α)/110249315139584

[16 5 32] 487 1488130731106797221/110249315139584 + (15062080632552069*α)/110249315139584

[248 -745 2240] 495 -438403246721012577/110249315139584 + (2923159514723199*α)/110249315139584

[124 -745 4480] 495 898189837707351327/110249315139584 + (3824481621811071*α)/110249315139584

[504 1257 3136] 495 725976166732944927/110249315139584 - (2351137701458049*α)/110249315139584

[6 9 96] 495 154011099215542215/13781164392448 + (1726823390848935*α)/13781164392448

[62 -311 1568] 495 97645464550031199/110249315139584 + (4976566423566207*α)/110249315139584

[52 -681 8928] 495 382630727795127903/110249315139584 - (4548819372460161*α)/110249315139584

[42 -87 192] 495 -154210831969844985/13781164392448 - (1631908200695385*α)/13781164392448

[42 -297 2112] 495 -154210831969844985/13781164392448 - (1631908200695385*α)/13781164392448

[36 -471 6176] 495 -168306726297937953/110249315139584 + (7868724311024511*α)/110249315139584

[56 151 416] 495 1258293940647404127/110249315139584 + (20635986127641471*α)/110249315139584

[16 23 64] 495 725976166732944927/110249315139584 - (2351137701458049*α)/110249315139584

[28 -87 288] 495 -616983933375885921/110249315139584 - (17777302025585793*α)/110249315139584

[142 343 832] 495 -1471566118502495841/110249315139584 - (17020463847158913*α)/110249315139584

[18 9 32] 495 -438403246721012577/110249315139584 + (2923159514723199*α)/110249315139584

[26 -265 2720] 495 1258293940647404127/110249315139584 + (20635986127641471*α)/110249315139584

[26 -343 4544] 495 -168306726297937953/110249315139584 + (7868724311024511*α)/110249315139584

[28 -151 832] 495 382630727795127903/110249315139584 - (4548819372460161*α)/110249315139584

[24 -105 480] 495 27244916004017415/13781164392448 - (220884813400665*α)/13781164392448

[2 4 256] 496 6942364088088/420567761 + (37675196184*α)/420567761

[250 748 2240] 496 6942364088088/420567761 + (37675196184*α)/420567761

[4 4 128] 496 749413916800/420567761 - (2879864704*α)/420567761

[124 -372 1120] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[124 -620 3104] 496 2111384649214/420567761 + (34427902334*α)/420567761

[124 -868 6080] 496 749413916800/420567761 - (2879864704*α)/420567761

[62 -124 256] 496 -4995900823576/420567761 - (31915466776*α)/420567761

[62 -372 2240] 496 -4995900823576/420567761 - (31915466776*α)/420567761

[8 4 64] 496 749413916800/420567761 - (2879864704*α)/420567761

[64 -196 608] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[64 -452 3200] 496 749413916800/420567761 - (2879864704*α)/420567761

[64 -708 7840] 496 2111384649214/420567761 + (34427902334*α)/420567761

[10 12 64] 496 2111384649214/420567761 + (34427902334*α)/420567761

[50 -252 1280] 496 2111384649214/420567761 + (34427902334*α)/420567761

[50 -452 4096] 496 2111384649214/420567761 + (34427902334*α)/420567761

[50 -652 8512] 496 2111384649214/420567761 + (34427902334*α)/420567761

[14 20 64] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[38 -196 1024] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[38 -348 3200] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[38 -500 6592] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[16 4 32] 496 6942364088088/420567761 + (37675196184*α)/420567761

[32 -68 160] 496 2111384649214/420567761 + (34427902334*α)/420567761

[32 -196 1216] 496 749413916800/420567761 - (2879864704*α)/420567761

[32 -324 3296] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[32 -452 6400] 496 749413916800/420567761 - (2879864704*α)/420567761

[16 68 320] 496 -973231632256/420567761 - (2879864704*α)/420567761

[56 -188 640] 496 -973231632256/420567761 - (2879864704*α)/420567761

[20 28 64] 496 749413916800/420567761 - (2879864704*α)/420567761

[28 -92 320] 496 -973231632256/420567761 - (2879864704*α)/420567761

[28 -148 800] 496 2111384649214/420567761 + (34427902334*α)/420567761

[28 -260 2432] 496 749413916800/420567761 - (2879864704*α)/420567761

[28 -316 3584] 496 -973231632256/420567761 - (2879864704*α)/420567761

[28 -372 4960] 496 -3610212482814/420567761 - (28668172926*α)/420567761

[28 -428 6560] 496 6942364088088/420567761 + (37675196184*α)/420567761

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

A nonlift newform in S₁₄(K(16))⁺