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

A nonlift newform in S₁₄(K(16))⁺

(Filename: eigs/eig-plus-14-16-3.html)

FORMULA FOR THE EIGENFORM f
with 3¹⁴⁻³λ₃ = -128952 - 3456*α,
where throughout this wepage, α is taken to have minimal polynomial -51 + 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	13704154507653534017181186807062984199696599596987965523637256189785101338513249056587045320911054500592499875339886859501184779881045637843424305051347723626546387998308052796444883566540801356489535585423354644452185622045309496657597106370565159839994231671803660399097128588340281213215368104913719765293321912821472902087317654195579832326865694899299785867847874274498736055242731139/139346163397515173007634508066265818182478979324098034182774656737401242465976868091571702593968373396189577525101994746516134309898121793180447242054183070104347549247298068126625751948766073776791699011298292519430410942159624926370286317846605362418888888504489739925894797501444709172222591956941205756282208356377530480369601906388496468551799394009088000000000 - (4452372556705757101254606878603988382895048008316414924643695794502287371502830051818798002767037818968774664144337039876042743505529146003356240616872055245985185788226804928707330456260498095629121437073383442303137042749715559990659467323757020575590624160278209817251851392732598853526537833030044503965306426168120016616034885503197329175906720219366405351579548964057492241028629311*α)/526418839501723986917730363805893090911587255224370351357148703230182471538134835012604209799436077274493959539274202375727618504059571218681689581093580487060868519378681590700586174028671834267879751820460216184514885781491916388509970534087175813582469134350294573053380346116568901317285347392888999523732787124092892925840718313023208881195686599589888000000000
b₂	-41168581080286909158699051727597963075806144942822269339145051079228348666413547553523525650338611044168754411926154820675529262876188293453370826035811514845255786084485052902964288778922988662993898924933046539198434784636254729545406550466094541782400445988434739773603882277222134191273580567544458804307949110503933507379870874410346920123737420991057598280916151543855753937436953343/348365408493787932519086270165664545456197448310245085456936641843503106164942170228929256484920933490473943812754986866290335774745304482951118105135457675260868873118245170316564379871915184441979247528245731298576027355399062315925715794616513406047222221261224349814736993753611772930556479892353014390705520890943826200924004765971241171379498485022720000000000 + (13379260321293198183404427626134390254557537621017690701399870741881076899219436155814852986493185399609517894800673426049411915043013124606643150912346363235101515514656904445948563149679985027055138825955287009552132433395273989816415473444096681005195046267761205878325855606173371203022728515606765976807652629352576294865370688433624176185513668957434043951681469903271068372055443307*α)/1316047098754309967294325909514732727278968138060925878392871758075456178845337087531510524498590193186234898848185505939319046260148928046704223952733951217652171298446703976751465435071679585669699379551150540461287214453729790971274926335217939533956172835875736432633450865291422253293213368482222498809331967810232232314601795782558022202989216498974720000000000
b₃	5513835476680635480740519427438905918026823006107312129506398062996168360182951692548921280055710105095950820342390413760837222648572629462040389283653733757989881986230847038469102289415885458007630564806888127984827843445980563114938478229315530666569860831921643682639489967376485751635817742320919628637048465521843003058112800850202441368972525540766756253484387158282948931843623769/34836540849378793251908627016566454545619744831024508545693664184350310616494217022892925648492093349047394381275498686629033577474530448295111810513545767526086887311824517031656437987191518444197924752824573129857602735539906231592571579461651340604722222126122434981473699375361177293055647989235301439070552089094382620092400476597124117137949848502272000000000 - (1791935312015122412990718339547576342115635900881656901763497644993688524808857695169251925578135404969602734711037743804395518567050074604165656809541905930413185394935016913944174933977145566085414748951558239186288807501002229809215915989291226134921933151483954872253612813622027351193067522588278457176730982822375822520657573975349415649606741873325547257475590718905064788742063181*α)/131604709875430996729432590951473272727896813806092587839287175807545617884533708753151052449859019318623489884818550593931904626014892804670422395273395121765217129844670397675146543507167958566969937955115054046128721445372979097127492633521793953395617283587573643263345086529142225329321336848222249880933196781023223231460179578255802220298921649897472000000000
b₄	7122468171233524165882663214391818161396941890585978305092340680495742563985222821063055474088891776538259609729504296181550720165054199228454854798799376289946280069498534914159800698043631397728642427416560903764882677719062390295038248965974851262481273328297435998007809175214803145818535706363378979192125104534761339084969589621993679663675960516254061965020690717009028348030663927/44789838234915591323882520449871155844368243354174368130177568237021827935492564743719475833775548591632364204497069739951614599610110576379429470660273129676397426543774379040701134554960523713968760396488736881245489231408450869190449173593551723634642857019300273547609042054035799376785833129016816135947852685978491940118800612767731007748792662360064000000000 - (2314719792722374284684567957625987734310454450965187973677595284902772712561649956871259251063096544105294310440642834162796487241098055692959337438812694918935762564770155058284058795968613362351385972878889452312694254972241807512076289645508742008990755556164996817912914624469613140471878799602271229049037721900171956282410317408516691812057977970727089694410456968046349850666457923*α)/169206055554125567223556188366179922078724474893547612936226368895415794422971911254051353149818739123944486994766707906483877376304862177433400222494365156555279166943147654153759841652073089586104205942290783773594070429765258839163919100242306511508650793184023255624300825537468575423413147376285749846914110147029858440448802314900317140384327835582464000000000
b₅	91764519830556821071844104374535297752303702040604962988126208841528051308918684145135133622428087762790554728101243689473049621884171132440911623247021825860879681797213966788447671865765117617062033139423358586299020057278892062239145353528327171468849520923773336498327987644663477328848302787831539156193988513178006952421966104121783327043306560152758819725460443417736171586106807/445248096063066233278832155951381904251707981272265908039634997859151899003713069641708398820964033336937111618669095639755695428076838865783677578161295016901465541973615128925313053564104614434719038260953124026582378158379866628638784684243591098853254436641564849467356157696923922798817749448214503599954985280732937629583343369525373331467288004526080000000 - (5040003886462189153585954678885089016438480802809597528370874778045845681645849366775287010759524294983630187160572738572067808065194053744574829204266482344675185793343881190351090917204409347755421234320698288589444727868391260155465030769255173534000546509535451051638671481142449436334318985170397621923773467089163135399901226879271174855667973117998265890708888295880177552485542267*α)/284266173330930952935574396455182269092257117821159989732860299744298534630592810906806273291695481728226738151208069282892913992192168458088112373790533463012869000464488058978316533975482790504655065983048516739638038322005634849795384088407074939334533332549159069448825386902947206711334087592160059742815705047010162179953987889032532795845670763778539520000000
b₆	2482457452179050977461204462908953824501584066429300210348511899486779625981376682503688525629749404163229252502764466649147331469784068074909267675803688607999102451247860399162032892998518090560221724770401945473975918377121810043665734339483627998102014421914000357306729166854707965953777970528660994083876112068668610966203888662746030131606953430211095477908992687053848360405489072781/18811732058664548356030658588945885454634662208753234614674578659549167732906877192362179850185730408485592965888769290779678131836246442079360377677314714464086919148385239197094476513083419959866879366525269490123105477191549365059988652909291723926549999948106114889995797662695035738250049914187062777098098128110966614849896257362447023254492918191226880000000000 - (62059628095808204398461087397446312632550391697299759347208288192500644970571225559429192864300977763462193316983843203921976569696456410811052471421652917782522564743949934809576930584740071999300763150682112059124752698440632656220359135125945746203439562803825031419274157597082813000498917084906600489273072650246203124194890166728608632599272046674753449692678261669623362894998280213*α)/5466657179440979864145661470291966713312636881176153648708851918159587204434477132823197563301836187081283425984770563132556038311387854963232930265202566596401326932009385749583010268759284432781828191981702244993039198500108362496065078623212979602587179472099212874015872825056677052141040146003078071977225097057887734229884382481394861458570591611125760000000000
b₇	221961700793741966806936903485559282529390067149411790208442758193208611099153345541935574862210527992472658439136984178518988913504187043308414073684553475385911876365669878201755809957031737939330281852255400533897460351765241345472343912949692166117712504585269692652074103915286090532264915278290183987360640039501404124469639940410257764412289925334896263197260173118474940409392871183/575869348734629031307060977212629146570448843125099018816568734475994930599190118133536117862828481892416111200676610942235044852129993124878378908489225952982252626991384873380443158563778162036741205097712331330299147260965796889591489374774236446731122447391003517040687683551888849130103568801644778890758105962580610658670293592727970099627334230343680000000000 - (72131665912855793200297823976770403867136589633965701886818481328032983503253640835482511792576078127792511911439939697222117599200906394681312680914617810104847883015487134610444339860348668960167418555198286429091349296081895847316745870212560416812892469495529866049418250651286243430983409673723372842947482570190640350196701034092648268639975584720291618517744410095158507144549377467*α)/2175506428553043007160008136136598998155028962917040737751481885798203071152496001837803111926240931593571975647000530226221280552491085138429431432070409155710732146411898410548340821240939723249911219258024362803352334096981899360678959860258226576539795912366013286598153471196024541158169037695102498031752844747526751377198886905861220376369929314631680000000000
b₈	166791967630245737616570822803176462975030968919704600248222121606344196967829044093876285307526394009435495953773057661558257478452991017543420629249934908645214471434047936944904417500906765605725077279064410310207005400608155405866118229066573259337724197370139100930833232376916312833003696156820378345818883450304971567874215002600162220685939176046453520924042054530091860579836147653/1881173205866454835603065858894588545463466220875323461467457865954916773290687719236217985018573040848559296588876929077967813183624644207936037767731471446408691914838523919709447651308341995986687936652526949012310547719154936505998865290929172392654999994810611488999579766269503573825004991418706277709809812811096661484989625736244702325449291819122688000000000 - (54206105042974877902854001610846824621295052258369545552418620048337028674333459099192761215322830393138882941074413805920443611856337824640346452123277198872496857474913685151480242238186892104368423685194010230851728695038220494071744827950828642574271471123571328497106971534621666157962823005812855234658496164859212401502631062132687106686507405928107919265034601315228108016402179497*α)/7106654333273273823389359911379556727306427945528999743321507493607463365764820272670156832292387043205668453780201732072322849804804211452202809344763336575321725011612201474457913349387069762616376649576212918490950958050140871244884602210176873483363333313728976736220634672573680167783352189804001493570392626175254054498849697225813319896141769094463488000000000
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c_1,38	8815570597093263151300016490756921776635232164930977713410054101919730645169436868565690939883232284229821618887741530481001160843718043842611269055269676969902750187081762119479769513784084822564159237231005219094802036742505341750171907881972821250520353794007973741984979/197072965283915863177229401570958002177708851127494904916455593735011366412503019181326596092542897859453778879066878074278623053791696057473036898070725655938471494405488109157304799089472452751558974515536189781872078037292198311297122037495929418814898353946782514119515412889600000000000 - (25292756237541069005483351670012430988337983290842978227553751869053117336147276034480866497578348446269485851890594703407281816004936165888330362107183312142324221529398594055260206935712379936313428077902685052659494751434147361370196540906107963337800987392359236060380989*α)/6700480819653139348025799653412572074042100938334826767159490186990386458025102652165104267146458527221428481888273854525473183828917665954083254534404672301908030809786595711348363169042063393553005133528230452583650653267934742584102149274861600239706544034190605480063524038246400000000000
c_1,39	-11917566792033494512612494947552401684965424035524473659674601286871007714999237981172982603357613878055355129387875998681587530433049341351243523310403545238194713053880147780528325944178037208972465113805236065962553227205390270766589021237062365597785706841992934934097297/3153167444542653810835670425135328034843341618039918478663289499760181862600048306901225537480686365751260462065070049188457968860667136919568590369131610495015543910487809746516876785431559244024943592248579036509953248596675172980753952599934870701038373663148520225912246606233600000000000 + (34718556767535733724241626494448535333038331568990779941075037117345286317561579027864205582155319032983417355551495332721274375727630871711403588596052451453647334535740884361921920233192421311528352386128720246784244470358069308619852610541594146730222613350259270501649977*α)/107207693114450229568412794454601153184673615013357228274551842991846183328401642434641668274343336435542855710212381672407570941262682655265332072550474756830528492956585531381573810704673014296848082136451687241338410452286955881345634388397785603835304704547049687681016384611942400000000000
c_1,40	-640716857003880179140493372619523276633088360419391509298017242550646494490389468804918837968096766228147711433092705710463797827829317878000240322150771778706971616301092657036522114295667666759962180323524906897154851795030572110697091711612788389742941523698072298127/7882918611356634527089176062838320087108354045099796196658223749400454656500120767253063843701715914378151155162675122971144922151667842298921475922829026237538859776219524366292191963578898110062358980621447591274883121491687932451884881499837176752595934157871300564780616515584000000000 + (58798629417561231228071492893200506228355305056913633399423689847270424149807062746397147935138653393460396510712698178195386619922904911366455579444268737508518498633419130243707216319697984369617560985811343912121405939566046597093738961347771604754590780164711752543399*α)/8576615449156018365473023556368092254773889201068578261964147439347694666272131394771333461947466914843428456816990533792605675301014612421226565804037980546442279436526842510525904856373841143747846570916134979307072836182956470507650751071822848306824376363763975014481310768955392000000000
c_1,41	2821145995063239314659818824078193949298128856950775763106208375159976881483137047758816525047160934860526607932400507805945737048680571096811079880516989506771520452748467912655062156815277974215876882051938379049499261749148269818597754913094999908467585704838951149796761/403605432901459687786965814417321988459947727109109565268901055969303278412806183283356868797527854816161339144328966296122620014165393525704779567248846143361989620542439647554160228535239583235192779807818116673274015820374422141536505932791663449732911828883010588916767565597900800000000000 - (8191593232249285743521018665365112612558921538641269846588806890939639839179847420748452431190794956777617851677753491152375627285045138548458801577865458925386961336374684732725232113585371249769482799860751129328186918786561106590514168985141878150534647626539561858245101*α)/13722584718649629384756837690188947607638222721709725219142635902956311466035410231634133539115947063749485530907184854068169080481623379873962505286460768874307647098442948016841447770198145829996554513465815966891316537892730352812241201714916557290919002182022360023170097230328627200000000000
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 51209/2980020224000 + (621*α)/745005056000

[8 -89 992] 15 4926167/2980020224000 + (223123*α)/745005056000

[4 -25 160] 15 3245191/2980020224000 + (184979*α)/745005056000

[12 -109 992] 23 -13179/6520832000 + (1449*α)/1630208000

[6 -13 32] 23 -13179/6520832000 + (1449*α)/1630208000

[6 -19 64] 23 -33888867/2980020224000 - (1881423*α)/745005056000

[14 -42 128] 28 -51209/727544000 - (621*α)/181886000

[14 -70 352] 28 -51209/727544000 - (621*α)/181886000

[8 -42 224] 28 -51209/727544000 - (621*α)/181886000

[8 -106 1408] 28 -51209/727544000 - (621*α)/181886000

[16 -113 800] 31 2985797/1490010112000 - (331407*α)/372502528000

[8 -113 1600] 31 2985797/1490010112000 - (331407*α)/372502528000

[14 -47 160] 31 -87957203/1490010112000 - (331407*α)/372502528000

[20 -101 512] 39 -32640603/2980020224000 - (7226007*α)/745005056000

[10 -91 832] 39 48281397/2980020224000 - (16442007*α)/745005056000

[10 -101 1024] 39 48281397/2980020224000 - (16442007*α)/745005056000

[8 -27 96] 39 2430204693/2980020224000 + (53978217*α)/745005056000

[24 -73 224] 47 -81779913/1490010112000 - (15632397*α)/372502528000

[12 -73 448] 47 -515589297/1490010112000 - (19950093*α)/372502528000

[4 9 32] 47 -81779913/1490010112000 - (15632397*α)/372502528000

[8 -73 672] 47 -515589297/1490010112000 - (19950093*α)/372502528000

[16 -55 192] 47 -4461789081/1490010112000 - (90133389*α)/372502528000

[2 4 32] 48 0

[26 76 224] 48 0

[6 12 32] 48 0

[14 36 96] 48 0

[2 3 32] 55 -1996557113/2980020224000 - (171865197*α)/745005056000

[14 -29 64] 55 64564939/596004044800 + (34948791*α)/149001011200

[14 -99 704] 55 64564939/596004044800 + (34948791*α)/149001011200

[8 -35 160] 55 2173438411/596004044800 - (1876041*α)/149001011200

[2 2 32] 60 116761/727544000 - (108691*α)/181886000

[30 -210 1472] 60 -3245191/727544000 - (184979*α)/181886000

[16 -50 160] 60 -4926167/727544000 - (223123*α)/181886000

[16 -178 1984] 60 -312843/145508800 - (29367*α)/36377200

[10 -30 96] 60 -8288119/727544000 - (299411*α)/181886000

[10 -50 256] 60 -4926167/727544000 - (223123*α)/181886000

[8 -50 320] 60 -6607143/727544000 - (261267*α)/181886000

[8 -114 1632] 60 -3245191/727544000 - (184979*α)/181886000

[2 1 32] 63 -11477782851/2980020224000 - (581349519*α)/745005056000

[16 -225 3168] 63 13127703117/2980020224000 + (601730673*α)/745005056000

[4 33 288] 63 13127703117/2980020224000 + (601730673*α)/745005056000

[12 -159 2112] 63 -880165359/372502528000 - (15540471*α)/93125632000

[8 -97 1184] 63 7085009181/2980020224000 + (871634289*α)/745005056000

[2 0 32] 64 100964/11367875 + (36864*α)/11367875

[2 8 64] 64 -50482/11367875 - (18432*α)/11367875

[2 16 160] 64 0

[4 8 32] 64 -50482/11367875 - (18432*α)/11367875

[20 56 160] 64 50482/11367875 + (18432*α)/11367875

[10 -24 64] 64 50482/11367875 + (18432*α)/11367875

[10 -64 416] 64 -100964/11367875 - (36864*α)/11367875

[10 -144 2080] 64 0

[36 -469 6112] 71 -6169830003/2980020224000 - (966398607*α)/745005056000

[18 -181 1824] 71 -6063539379/2980020224000 - (1017918351*α)/745005056000

[18 -235 3072] 71 -18859560531/2980020224000 - (360695439*α)/745005056000

[12 -85 608] 71 -6063539379/2980020224000 - (1017918351*α)/745005056000

[120 277 640] 71 -6169830003/2980020224000 - (966398607*α)/745005056000

[10 -43 192] 71 -6593824227/2980020224000 - (7909263*α)/745005056000

[10 -53 288] 71 -18859560531/2980020224000 - (360695439*α)/745005056000

[40 -441 4864] 79 7271014193/1490010112000 - (838967283*α)/372502528000

[20 -121 736] 79 -8237802891/298002022400 - (411725079*α)/74500505600

[190 441 1024] 79 7271014193/1490010112000 - (838967283*α)/372502528000

[10 -71 512] 79 -8237802891/298002022400 - (411725079*α)/74500505600

[10 -121 1472] 79 -18230861591/1490010112000 - (2370894579*α)/372502528000

[44 -397 3584] 87 -94528123457/2980020224000 - (5712786133*α)/745005056000

[22 -45 96] 87 29575025279/2980020224000 + (3293649451*α)/745005056000

[22 -243 2688] 87 -233845177/6520832000 - (11888813*α)/1630208000

[16 -115 832] 87 29575025279/2980020224000 + (3293649451*α)/745005056000

[12 -51 224] 87 -33509372413/596004044800 + (219630703*α)/149001011200

[134 307 704] 87 -94528123457/2980020224000 - (5712786133*α)/745005056000

[46 -138 416] 92 -21843261/727544000 - (3205809*α)/181886000

[46 -230 1152] 92 -21843261/727544000 - (3205809*α)/181886000

[4 6 32] 92 -21843261/727544000 - (3205809*α)/181886000

[24 -218 1984] 92 33888867/727544000 + (1881423*α)/181886000

[26 70 192] 92 33888867/727544000 + (1881423*α)/181886000

[162 374 864] 92 -21843261/727544000 - (3205809*α)/181886000

[6 26 128] 92 33888867/727544000 + (1881423*α)/181886000

[26 -86 288] 92 17924199/145508800 + (1393731*α)/36377200

[12 -26 64] 92 33888867/727544000 + (1881423*α)/181886000

[12 -38 128] 92 -21843261/727544000 - (3205809*α)/181886000

[12 -122 1248] 92 33888867/727544000 + (1881423*α)/181886000

[12 -134 1504] 92 33888867/727544000 + (1881423*α)/181886000

[48 -337 2368] 95 -223192718481/2980020224000 - (11534995989*α)/745005056000

[24 -337 4736] 95 301565753103/2980020224000 + (16009206507*α)/745005056000

[4 17 96] 95 -296326150497/2980020224000 - (13610671893*α)/745005056000

[16 -81 416] 95 -296326150497/2980020224000 - (13610671893*α)/745005056000

[6 49 416] 95 301565753103/2980020224000 + (16009206507*α)/745005056000

[12 -145 1760] 95 735280927791/2980020224000 + (21847814379*α)/745005056000

[60 145 352] 95 -95495971041/2980020224000 - (1713412629*α)/745005056000

[10 15 32] 95 -223192718481/2980020224000 - (11534995989*α)/745005056000

[52 -261 1312] 103 -32256527703/2980020224000 - (9941519907*α)/745005056000

[4 5 32] 103 -32256527703/2980020224000 - (9941519907*α)/745005056000

[26 -261 2624] 103 -2370690411/596004044800 - (825335559*α)/149001011200

[14 -59 256] 103 -460156837543/2980020224000 - (22115544867*α)/745005056000

[14 -101 736] 103 -2370690411/596004044800 - (825335559*α)/149001011200

[56 -169 512] 111 89559821649/2980020224000 - (5322269019*α)/745005056000

[28 -169 1024] 111 -127874137587/596004044800 - (6805959903*α)/149001011200

[120 297 736] 111 -125265334671/2980020224000 + (8227604901*α)/745005056000

[6 9 32] 111 89559821649/2980020224000 - (5322269019*α)/745005056000

[14 -169 2048] 111 -1113545029599/2980020224000 - (31046301531*α)/745005056000

[14 -183 2400] 111 -1208088127503/2980020224000 - (34681942107*α)/745005056000

[12 -87 640] 111 -127874137587/596004044800 - (6805959903*α)/149001011200

[10 23 64] 111 -125265334671/2980020224000 + (8227604901*α)/745005056000

[2 4 64] 112 0

[58 172 512] 112 0

[4 4 32] 112 0

[28 -84 256] 112 0

[28 -140 704] 112 0

[28 -196 1376] 112 0

[14 -28 64] 112 0

[14 -84 512] 112 0

[8 12 32] 112 0

[16 -84 448] 112 0

[16 -148 1376] 112 0

[16 -212 2816] 112 0

[2 3 64] 119 -27908184717/1490010112000 - (2481776073*α)/372502528000

[30 -61 128] 119 -53336981577/298002022400 - (984266613*α)/74500505600

[30 -451 6784] 119 -27908184717/1490010112000 - (2481776073*α)/372502528000

[20 -61 192] 119 -151512950193/298002022400 - (4095964917*α)/74500505600

[90 221 544] 119 -64568462637/1490010112000 + (11477451447*α)/372502528000

[16 -67 288] 119 718726129467/1490010112000 + (24521072823*α)/372502528000

[8 67 576] 119 -53336981577/298002022400 - (984266613*α)/74500505600

[12 -61 320] 119 -151512950193/298002022400 - (4095964917*α)/74500505600

[24 61 160] 119 -568345817973/1490010112000 - (19372062537*α)/372502528000

[12 -125 1312] 119 -64568462637/1490010112000 + (11477451447*α)/372502528000

[2 2 64] 124 -93928797/363772000 + (331407*α)/90943000

[62 -434 3040] 124 -93928797/363772000 + (331407*α)/90943000

[4 2 32] 124 -93928797/363772000 + (331407*α)/90943000

[32 -226 1600] 124 87957203/363772000 + (331407*α)/90943000

[16 -98 608] 124 87957203/363772000 + (331407*α)/90943000

[16 -226 3200] 124 87957203/363772000 + (331407*α)/90943000

[8 34 160] 124 87957203/363772000 + (331407*α)/90943000

[28 -94 320] 124 -93928797/363772000 + (331407*α)/90943000

[10 14 32] 124 -93928797/363772000 + (331407*α)/90943000

[14 -46 160] 124 269843203/363772000 + (331407*α)/90943000

[14 -130 1216] 124 87957203/363772000 + (331407*α)/90943000

[14 -158 1792] 124 87957203/363772000 + (331407*α)/90943000

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[10 13 64] 471 -641718898814901/2980020224000 + (38268160451031*α)/745005056000

[10 83 736] 471 5564373989872683/2980020224000 + (305371186573527*α)/745005056000

[40 -563 7936] 471 5564373989872683/2980020224000 + (305371186573527*α)/745005056000

[12 51 256] 471 1226853985009083/2980020224000 + (27592136903127*α)/745005056000

[30 -333 3712] 471 1226853985009083/2980020224000 + (27592136903127*α)/745005056000

[24 -51 128] 471 203731879643199/596004044800 + (13406947148331*α)/149001011200

[50 -173 608] 471 4672325387377563/2980020224000 + (271171291340247*α)/745005056000

[26 -371 5312] 471 -3547470094030821/2980020224000 - (61168887793449*α)/745005056000

[26 -397 6080] 471 3342804103331307/2980020224000 + (93039350061783*α)/745005056000

[238 -714 2144] 476 298174533681/72754400 + (7360659189*α)/18188600

[238 -1190 5952] 476 1013319222069/363772000 + (31924181961*α)/90943000

[4 6 128] 476 53336981577/72754400 + (984266613*α)/18188600

[120 -1082 9760] 476 53336981577/72754400 + (984266613*α)/18188600

[90 262 768] 476 568345817973/363772000 + (19372062537*α)/90943000

[738 1718 4000] 476 189907951989/363772000 + (17156538441*α)/90943000

[6 26 192] 476 -628427825691/363772000 - (43434727479*α)/90943000

[90 -278 864] 476 -628427825691/363772000 - (43434727479*α)/90943000

[60 -122 256] 476 -191500570527/72754400 - (5392125963*α)/18188600

[60 -422 2976] 476 -210868538451/363772000 + (42219081*α)/90943000

[60 -602 6048] 476 -479949406299/363772000 - (22081515831*α)/90943000

[60 -902 13568] 476 53336981577/72754400 + (984266613*α)/18188600

[10 22 96] 476 -628427825691/363772000 - (43434727479*α)/90943000

[210 518 1280] 476 151512950193/72754400 + (4095964917*α)/18188600

[10 42 224] 476 327955994457/72754400 + (10708972533*α)/18188600

[62 -198 640] 476 1261342106301/363772000 + (51329338569*α)/90943000

[40 -122 384] 476 -24930094071/72754400 - (2517042699*α)/18188600

[40 -442 4896] 476 1261342106301/363772000 + (51329338569*α)/90943000

[12 26 96] 476 -628427825691/363772000 - (43434727479*α)/90943000

[180 442 1088] 476 151512950193/72754400 + (4095964917*α)/18188600

[34 -102 320] 476 253787395629/363772000 - (10369689399*α)/90943000

[34 -170 864] 476 327955994457/72754400 + (10708972533*α)/18188600

[30 -122 512] 476 -718726129467/363772000 - (24521072823*α)/90943000

[30 -182 1120] 476 -210868538451/363772000 + (42219081*α)/90943000

[30 -362 4384] 476 -2689548204171/363772000 - (83405884599*α)/90943000

[30 -422 5952] 476 -210868538451/363772000 + (42219081*α)/90943000

[16 6 32] 476 1013319222069/363772000 + (31924181961*α)/90943000

[32 -134 576] 476 1252095945237/363772000 + (34363738953*α)/90943000

[32 -390 4768] 476 -718726129467/363772000 - (24521072823*α)/90943000

[16 134 1152] 476 -191500570527/72754400 - (5392125963*α)/18188600

[18 26 64] 476 53336981577/72754400 + (984266613*α)/18188600

[30 -218 1600] 476 -479949406299/363772000 - (22081515831*α)/90943000

[30 -278 2592] 476 -210868538451/363772000 + (42219081*α)/90943000

[30 -458 7008] 476 298174533681/72754400 + (7360659189*α)/18188600

[24 -122 640] 476 -24930094071/72754400 - (2517042699*α)/18188600

[24 -314 4128] 476 253787395629/363772000 - (10369689399*α)/90943000

[48 122 320] 476 946783683957/363772000 + (21587586633*α)/90943000

[248 570 1312] 476 568345817973/363772000 + (19372062537*α)/90943000

[24 -58 160] 476 151512950193/72754400 + (4095964917*α)/18188600

[24 -250 2624] 476 151512950193/72754400 + (4095964917*α)/18188600

[240 -1681 11776] 479 129594031505133/372502528000 + (19496807317827*α)/93125632000

[120 -1681 23552] 479 -370018968858471/372502528000 - (9371101059549*α)/93125632000

[4 17 192] 479 396232386227661/372502528000 + (29871847582659*α)/93125632000

[80 -401 2016] 479 1016967657911937/372502528000 + (6225865476003*α)/93125632000

[6 49 480] 479 148988338604553/372502528000 - (9329350653693*α)/93125632000

[60 -721 8672] 479 -1184053461452061/372502528000 - (58244866276509*α)/93125632000

[8 17 96] 479 1016967657911937/372502528000 + (6225865476003*α)/93125632000

[48 -145 448] 479 -855167336152851/372502528000 - (16452248230269*α)/93125632000

[10 81 704] 479 54864309860487/74500505600 + (5989060184103*α)/18625126400

[40 -401 4032] 479 -105161271588441/372502528000 - (10698037943229*α)/93125632000

[54 -175 576] 479 -138263159333757/372502528000 - (19596738978333*α)/93125632000

[12 17 64] 479 396232386227661/372502528000 + (29871847582659*α)/93125632000

[42 -593 8384] 479 54864309860487/74500505600 + (5989060184103*α)/18625126400

[36 -401 4480] 479 -138263159333757/372502528000 - (19596738978333*α)/93125632000

[178 433 1056] 479 -101173545028323/372502528000 - (1204405285437*α)/93125632000

[30 -271 2464] 479 -105161271588441/372502528000 - (10698037943229*α)/93125632000

[28 -145 768] 479 -855167336152851/372502528000 - (16452248230269*α)/93125632000

[56 145 384] 479 101261679095541/372502528000 + (6775596161379*α)/93125632000

[24 -145 896] 479 101261679095541/372502528000 + (6775596161379*α)/93125632000

[20 81 352] 479 -12905101052109/372502528000 + (7741507567779*α)/93125632000

[28 -401 5760] 479 148988338604553/372502528000 - (9329350653693*α)/93125632000

[168 401 960] 479 -101173545028323/372502528000 - (1204405285437*α)/93125632000

[24 -367 5632] 479 129594031505133/372502528000 + (19496807317827*α)/93125632000

[60 -209 736] 479 -12905101052109/372502528000 + (7741507567779*α)/93125632000

[244 -1221 6112] 487 -3079428634909487/2980020224000 - (63794983936203*α)/745005056000

[4 5 128] 487 -816606792542111/2980020224000 + (59700848831541*α)/745005056000

[122 -1221 12224] 487 10222948889092849/2980020224000 + (265672956233781*α)/745005056000

[62 -933 14048] 487 -816606792542111/2980020224000 + (59700848831541*α)/745005056000

[16 5 32] 487 -3079428634909487/2980020224000 - (63794983936203*α)/745005056000

[248 -745 2240] 495 -6818142936778413/2980020224000 - (86997296790897*α)/745005056000

[124 -745 4480] 495 -1169018430933417/596004044800 + (17673738954627*α)/149001011200

[504 1257 3136] 495 -3601394942979981/2980020224000 - (23260511781489*α)/745005056000

[6 9 96] 495 47328640185663/372502528000 + (2985923278647*α)/93125632000

[62 -311 1568] 495 -19422995683015581/2980020224000 - (209204847947889*α)/745005056000

[52 -681 8928] 495 15621578914553763/2980020224000 + (288018219676047*α)/745005056000

[42 -87 192] 495 -4120689304989/74500505600 - (570312575541*α)/18625126400

[42 -297 2112] 495 -4120689304989/74500505600 - (570312575541*α)/18625126400

[36 -471 6176] 495 3570017573950503/596004044800 + (80391234136707*α)/149001011200

[56 151 416] 495 -4465269241211229/2980020224000 - (430803596102001*α)/745005056000

[16 23 64] 495 -3601394942979981/2980020224000 - (23260511781489*α)/745005056000

[28 -87 288] 495 -7705318314247149/2980020224000 - (286921345754481*α)/745005056000

[142 343 832] 495 17204307294564627/2980020224000 + (379474909150863*α)/745005056000

[18 9 32] 495 -6818142936778413/2980020224000 - (86997296790897*α)/745005056000

[26 -265 2720] 495 -4465269241211229/2980020224000 - (430803596102001*α)/745005056000

[26 -343 4544] 495 3570017573950503/596004044800 + (80391234136707*α)/149001011200

[28 -151 832] 495 15621578914553763/2980020224000 + (288018219676047*α)/745005056000

[24 -105 480] 495 -34868322005661/74500505600 - (204491443509*α)/18625126400

[2 4 256] 496 1024

[250 748 2240] 496 -1024

[4 4 128] 496 -1024

[124 -372 1120] 496 2615351552/2273575 - (247938048*α)/2273575

[124 -620 3104] 496 2040930048/2273575 + (247938048*α)/2273575

[124 -868 6080] 496 -1024

[62 -124 256] 496 1024

[62 -372 2240] 496 -1024

[8 4 64] 496 -1024

[64 -196 608] 496 -287210752/2273575 + (247938048*α)/2273575

[64 -452 3200] 496 1024

[64 -708 7840] 496 287210752/2273575 - (247938048*α)/2273575

[10 12 64] 496 2040930048/2273575 + (247938048*α)/2273575

[50 -252 1280] 496 287210752/2273575 - (247938048*α)/2273575

[50 -452 4096] 496 -2615351552/2273575 + (247938048*α)/2273575

[50 -652 8512] 496 287210752/2273575 - (247938048*α)/2273575

[14 20 64] 496 2615351552/2273575 - (247938048*α)/2273575

[38 -196 1024] 496 -287210752/2273575 + (247938048*α)/2273575

[38 -348 3200] 496 -2040930048/2273575 - (247938048*α)/2273575

[38 -500 6592] 496 -287210752/2273575 + (247938048*α)/2273575

[16 4 32] 496 1024

[32 -68 160] 496 -2615351552/2273575 + (247938048*α)/2273575

[32 -196 1216] 496 1024

[32 -324 3296] 496 -2040930048/2273575 - (247938048*α)/2273575

[32 -452 6400] 496 1024

[16 68 320] 496 0

[56 -188 640] 496 -2048

[20 28 64] 496 -1024

[28 -92 320] 496 2048

[28 -148 800] 496 287210752/2273575 - (247938048*α)/2273575

[28 -260 2432] 496 1024

[28 -316 3584] 496 0

[28 -372 4960] 496 -287210752/2273575 + (247938048*α)/2273575

[28 -428 6560] 496 -1024

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

A nonlift newform in S₁₄(K(16))⁺