Properties

Label 1.94.a
Level 1
Weight 94
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 94 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{94}(\Gamma_0(1))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

Trace form

\(7q \) \(\mathstrut +\mathstrut 43735426713792q^{2} \) \(\mathstrut -\mathstrut 3678766354327579216884q^{3} \) \(\mathstrut +\mathstrut 37433779444352805880587218944q^{4} \) \(\mathstrut -\mathstrut 242501922056818695041616562179750q^{5} \) \(\mathstrut -\mathstrut 3422349689703076907975614807426150656q^{6} \) \(\mathstrut -\mathstrut 921137753903839555947108372394316103208q^{7} \) \(\mathstrut +\mathstrut 628568314501252186502498490389635108700160q^{8} \) \(\mathstrut +\mathstrut 362824653360866901561998689210341299050559211q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 43735426713792q^{2} \) \(\mathstrut -\mathstrut 3678766354327579216884q^{3} \) \(\mathstrut +\mathstrut 37433779444352805880587218944q^{4} \) \(\mathstrut -\mathstrut 242501922056818695041616562179750q^{5} \) \(\mathstrut -\mathstrut 3422349689703076907975614807426150656q^{6} \) \(\mathstrut -\mathstrut 921137753903839555947108372394316103208q^{7} \) \(\mathstrut +\mathstrut 628568314501252186502498490389635108700160q^{8} \) \(\mathstrut +\mathstrut 362824653360866901561998689210341299050559211q^{9} \) \(\mathstrut +\mathstrut 56663128890275718532856219951648854919834448000q^{10} \) \(\mathstrut +\mathstrut 1081566396126190174166498109003279139923369012324q^{11} \) \(\mathstrut -\mathstrut 163904625261310040243241458042755377696324875010048q^{12} \) \(\mathstrut +\mathstrut 1923851638471797431690458036346871401286646408469426q^{13} \) \(\mathstrut -\mathstrut 827492161115181455891429526236298470299001717526508032q^{14} \) \(\mathstrut -\mathstrut 16711611501720521025854082681912174509227777477242411000q^{15} \) \(\mathstrut -\mathstrut 183863117199568288307852091185855957272115704336744448q^{16} \) \(\mathstrut +\mathstrut 809325537307953309871783611300921224816172571619454935742q^{17} \) \(\mathstrut +\mathstrut 79483944128603792717921302063558947044650774054000109708736q^{18} \) \(\mathstrut -\mathstrut 491316328040151561437984621759105514680907320256463264658500q^{19} \) \(\mathstrut -\mathstrut 5819101371751539891329503686613738398860076574931824253952000q^{20} \) \(\mathstrut +\mathstrut 54451750333719895476183963426175615210898459319681281516277984q^{21} \) \(\mathstrut +\mathstrut 341061341496448817039487179432626029859991533289656810924326144q^{22} \) \(\mathstrut -\mathstrut 2595697104202345855126053487687658963668179272707633091075699064q^{23} \) \(\mathstrut -\mathstrut 29432689846399066174371175818785662556182882963620634526849433600q^{24} \) \(\mathstrut +\mathstrut 184388886386678531186865888507627315189418933935123407708899515625q^{25} \) \(\mathstrut +\mathstrut 793059166145746283698718389909557916534745558035448772312212840064q^{26} \) \(\mathstrut -\mathstrut 10506923232698637098067136941837198924358450251426727402321208664840q^{27} \) \(\mathstrut +\mathstrut 1916814131388145595393790805747801246689773266225672358812878209024q^{28} \) \(\mathstrut +\mathstrut 115585291038420509795092429775705167101645550654624527668945364036450q^{29} \) \(\mathstrut -\mathstrut 646359246874848354315998274237243944693324584248820365706098812352000q^{30} \) \(\mathstrut -\mathstrut 1163635467946810748613893942791764663199899897323284701513531956983456q^{31} \) \(\mathstrut -\mathstrut 7066990866795922437106429389517828098400874624281122281464920526553088q^{32} \) \(\mathstrut +\mathstrut 66569296470254314915045188377632673804554883301553196046747543676316112q^{33} \) \(\mathstrut +\mathstrut 80911624156374405155780927188384543491071504244617539921495324380294528q^{34} \) \(\mathstrut -\mathstrut 1672188852118103650980495790489284130570309869892526153633308501275462000q^{35} \) \(\mathstrut +\mathstrut 5276416924359744904633666070671763693285317535397001093231145577416896512q^{36} \) \(\mathstrut +\mathstrut 11072759435314078994932599484815080247923078570346623467670584315337670842q^{37} \) \(\mathstrut -\mathstrut 42692186143014046654789275667852179938472092905944200699148410427788924160q^{38} \) \(\mathstrut -\mathstrut 205635087839752927920079557406846610376307390801963146422737416149757222168q^{39} \) \(\mathstrut +\mathstrut 760187696799287916151508882607919116749295190931669242261910585944965120000q^{40} \) \(\mathstrut -\mathstrut 509603803596826806676973650829096820638503322986104149790656476262528674746q^{41} \) \(\mathstrut -\mathstrut 542653738615875619591084295077236547022836265832353730045755853854336280576q^{42} \) \(\mathstrut -\mathstrut 7275658116979055674748970912580687053338617746072325435955591393683798211644q^{43} \) \(\mathstrut +\mathstrut 9423347779397833928027118997217234224491886242773059800183027480258516369408q^{44} \) \(\mathstrut +\mathstrut 164505351109492760826482356226220602919737242087979463171032783958351054923250q^{45} \) \(\mathstrut -\mathstrut 639778771092842366359510076082228574613573083413403803040568658686807125218816q^{46} \) \(\mathstrut -\mathstrut 371149830895115606730684780470708713676568637183334957675426341554516993409008q^{47} \) \(\mathstrut -\mathstrut 416843258596979693775599022471376378646238618283847940753742770006189894795264q^{48} \) \(\mathstrut +\mathstrut 2561975156227711495237514871966779964501558283497058708235084248829398599957999q^{49} \) \(\mathstrut -\mathstrut 31492320141514234591073138519794385457712593727985587891779934655429621403000000q^{50} \) \(\mathstrut -\mathstrut 55702073279983479511744597938778959921377812834972727705529236388320801422608936q^{51} \) \(\mathstrut -\mathstrut 55278983045853834535146427408736596689073596604984335518990233309047240924848128q^{52} \) \(\mathstrut -\mathstrut 363766241548602923075270727552075967170433033161760056492510229436384310833635734q^{53} \) \(\mathstrut -\mathstrut 1988318954489765046302005332528558912554496159988340641069330680002958019070937600q^{54} \) \(\mathstrut -\mathstrut 3520855393890604949232827617669938515471701214675853816941159595183623184386577000q^{55} \) \(\mathstrut -\mathstrut 12936956692485908268365121199611114191360014164491088694387999166431300696512921600q^{56} \) \(\mathstrut -\mathstrut 13862265625178226892264597068584427924864963571452022505627535112981742091059296080q^{57} \) \(\mathstrut -\mathstrut 73663001170657752665346575473371223431752845037418753763472734766611572171441325440q^{58} \) \(\mathstrut -\mathstrut 119839908140624573484226478891501296275544385047787439213910489726968365086286210700q^{59} \) \(\mathstrut -\mathstrut 468107546718994029022024884762568911834725078620349067042941227204209206458724352000q^{60} \) \(\mathstrut -\mathstrut 328281166748320542242523532793984772143143166398612931227281116669834617338050603326q^{61} \) \(\mathstrut -\mathstrut 999402477792071119370831029463209574610493980381087626216590758004912070795081435136q^{62} \) \(\mathstrut -\mathstrut 2240117215552784969170617635914585450026055291898885166701984645532069514866650525064q^{63} \) \(\mathstrut -\mathstrut 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616q^{64} \) \(\mathstrut +\mathstrut 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500q^{65} \) \(\mathstrut +\mathstrut 12481418287827593167181900965724458478832175604254852160085986797561206241884769502208q^{66} \) \(\mathstrut +\mathstrut 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492q^{67} \) \(\mathstrut +\mathstrut 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624q^{68} \) \(\mathstrut +\mathstrut 125665844363573358610510037253282595268580727449546920119880250916295279742987985413792q^{69} \) \(\mathstrut +\mathstrut 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000q^{70} \) \(\mathstrut +\mathstrut 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984q^{71} \) \(\mathstrut +\mathstrut 1153857576733974210773243583317262094473717150308417455216249971043377175999426453831680q^{72} \) \(\mathstrut +\mathstrut 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686q^{73} \) \(\mathstrut +\mathstrut 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848q^{74} \) \(\mathstrut +\mathstrut 944080624555199942138536838755965622984512203073943882229003778583589699488457416312500q^{75} \) \(\mathstrut -\mathstrut 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600q^{76} \) \(\mathstrut -\mathstrut 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856q^{77} \) \(\mathstrut -\mathstrut 73115054525877473148472082243219461137606249175371809547554984327725748004401082971708928q^{78} \) \(\mathstrut -\mathstrut 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200q^{79} \) \(\mathstrut -\mathstrut 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000q^{80} \) \(\mathstrut -\mathstrut 70612572309757383558801217018071484518377724651384007545224773102476238636837549694743953q^{81} \) \(\mathstrut -\mathstrut 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376q^{82} \) \(\mathstrut -\mathstrut 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004q^{83} \) \(\mathstrut +\mathstrut 1649840105905513745515070352659141454913812021851911846045941535531840033929951137654243328q^{84} \) \(\mathstrut +\mathstrut 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500q^{85} \) \(\mathstrut +\mathstrut 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224q^{86} \) \(\mathstrut +\mathstrut 6559051070263618632233284423714108103382010904819072234989172243851503736785525745425626280q^{87} \) \(\mathstrut +\mathstrut 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120q^{88} \) \(\mathstrut +\mathstrut 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350q^{89} \) \(\mathstrut +\mathstrut 19840068851074490675120863444780810644229753682905466429373855007108663777299926218608144000q^{90} \) \(\mathstrut -\mathstrut 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496q^{91} \) \(\mathstrut -\mathstrut 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808q^{92} \) \(\mathstrut -\mathstrut 125975338781791055721238628453160089358246167768072651306884109747935024714536192316708787328q^{93} \) \(\mathstrut -\mathstrut 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392q^{94} \) \(\mathstrut -\mathstrut 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000q^{95} \) \(\mathstrut -\mathstrut 229425406959806321843310706398725653116223652026933598684053060220054993118393316925679599616q^{96} \) \(\mathstrut +\mathstrut 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342q^{97} \) \(\mathstrut -\mathstrut 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256q^{98} \) \(\mathstrut +\mathstrut 306809773352993420176583539450272713060724644284625495060244639714128125893072287559839588052q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{94}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.94.a.a \(7\) \(54.773\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(43\!\cdots\!92\) \(-3\!\cdots\!84\) \(-2\!\cdots\!50\) \(-9\!\cdots\!08\) \(+\) \(q+(6247918101970+\beta _{1})q^{2}+\cdots\)