Properties

Label 1.114.a
Level 1
Weight 114
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 114 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{114}(\Gamma_0(1))\).

Total New Old
Modular forms 10 10 0
Cusp forms 9 9 0
Eisenstein series 1 1 0

Trace form

\(9q \) \(\mathstrut +\mathstrut 4973724357874032q^{2} \) \(\mathstrut -\mathstrut 1047822666262699970761104924q^{3} \) \(\mathstrut +\mathstrut 57140122287714158706660944854495488q^{4} \) \(\mathstrut -\mathstrut 3116148576934475303759287082847998426250q^{5} \) \(\mathstrut -\mathstrut 8679197271676415971774420800017032303605312q^{6} \) \(\mathstrut -\mathstrut 175592521264923853936268390919613238158926276408q^{7} \) \(\mathstrut -\mathstrut 1152754689437068715781677022006928573086863264747520q^{8} \) \(\mathstrut +\mathstrut 551049940125998155825143115188713609620516409643418677q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 4973724357874032q^{2} \) \(\mathstrut -\mathstrut 1047822666262699970761104924q^{3} \) \(\mathstrut +\mathstrut 57140122287714158706660944854495488q^{4} \) \(\mathstrut -\mathstrut 3116148576934475303759287082847998426250q^{5} \) \(\mathstrut -\mathstrut 8679197271676415971774420800017032303605312q^{6} \) \(\mathstrut -\mathstrut 175592521264923853936268390919613238158926276408q^{7} \) \(\mathstrut -\mathstrut 1152754689437068715781677022006928573086863264747520q^{8} \) \(\mathstrut +\mathstrut 551049940125998155825143115188713609620516409643418677q^{9} \) \(\mathstrut -\mathstrut 153264347969576737314363653067831776074945972002322140000q^{10} \) \(\mathstrut +\mathstrut 124303845165751869554468963179928310347446325358753066991788q^{11} \) \(\mathstrut -\mathstrut 4766393536299397973462835582969587848650683059861216359840768q^{12} \) \(\mathstrut +\mathstrut 118066950692074908165278563837084569941718111528864100316810046q^{13} \) \(\mathstrut +\mathstrut 23370095428037254282484566813709955199818716752021690625741210496q^{14} \) \(\mathstrut -\mathstrut 801369990352485680694849420185298838396866837392656002948893145000q^{15} \) \(\mathstrut +\mathstrut 109009769902909383382120055717425408918319663897461125806267782201344q^{16} \) \(\mathstrut +\mathstrut 1031208472354491758575110721181756882175051278670426497304478795027362q^{17} \) \(\mathstrut +\mathstrut 21853761778376511004199260652941739695840479087427332697148033133176496q^{18} \) \(\mathstrut -\mathstrut 2054770397164032300993860357285529834117448193071848654506031346813189260q^{19} \) \(\mathstrut -\mathstrut 128965280615606341221181395517996603639092921677759187360515198160536640000q^{20} \) \(\mathstrut -\mathstrut 2051981423257402292087521454906945230917134727108225442350522950612144271072q^{21} \) \(\mathstrut -\mathstrut 31233703450481121590220064319836416371256690633810598891839492722859409642176q^{22} \) \(\mathstrut -\mathstrut 167806258064059379045373533912927060845638327737895149615950186261514952182184q^{23} \) \(\mathstrut +\mathstrut 837647327683589821169163577629460913691878109446800095361456758053616583557120q^{24} \) \(\mathstrut +\mathstrut 36110808046585671891862329281725549351642982282250931138010564349682541171484375q^{25} \) \(\mathstrut +\mathstrut 273284118611845700597932385482119882778869175349924218776704957190525454972143648q^{26} \) \(\mathstrut -\mathstrut 1293409658858973603349494974301711616276027502548100865754773226934344693652580120q^{27} \) \(\mathstrut -\mathstrut 12449742560521692406151296738508394024549837700960492852336353346600639157797779456q^{28} \) \(\mathstrut +\mathstrut 16393803312375561825707281499219064392567318107169713827635118635692166495008904910q^{29} \) \(\mathstrut +\mathstrut 1444554724925215896891120206778115916774229741452396468041800381952830143736681360000q^{30} \) \(\mathstrut +\mathstrut 1314403569804018815618492241812394006579677928452900483535632508652944766037998410528q^{31} \) \(\mathstrut -\mathstrut 21448902248775261233416755741924844958908937761160756654268584846741870841621352808448q^{32} \) \(\mathstrut -\mathstrut 211847819746714833550323551974005344232426451287015334370441057211901425852772059609168q^{33} \) \(\mathstrut +\mathstrut 319367478280300365454292314290661290493902375851140946818660251269274780967076833561056q^{34} \) \(\mathstrut +\mathstrut 3439596420817236254046899424410940097643944233598368039111722250253904941775326256910000q^{35} \) \(\mathstrut +\mathstrut 2704504833410501582895107271001450900815653199167021310209481973200374905160451231300864q^{36} \) \(\mathstrut -\mathstrut 59867320490204404665587120670290466524223984034118562335350833430431530376567774885723498q^{37} \) \(\mathstrut -\mathstrut 82453523727277361450274687052865709436318494611960850831592535368825105943678502733442880q^{38} \) \(\mathstrut +\mathstrut 871232822588974033828162396761465282346428529310140460376676860192325312944522604565747064q^{39} \) \(\mathstrut +\mathstrut 6827166757827354756060064429590450961456578801730020944860911233033409499443258590438400000q^{40} \) \(\mathstrut -\mathstrut 34550149215769251780094496181290849916810545798144119670305052821692690196704735942577072902q^{41} \) \(\mathstrut -\mathstrut 106065652173490837329551409984862217118049589651335199831107089722564993162529690865908896256q^{42} \) \(\mathstrut +\mathstrut 207231754793163377176542763271534728167453514398489730764515211376339059665627233099893879756q^{43} \) \(\mathstrut +\mathstrut 2312703333865421082227940066456566870684549523781445620538452769155749838714861346004252527616q^{44} \) \(\mathstrut +\mathstrut 256198961065429853532686454584243663537866293764106258783025404071252757628746328749329658750q^{45} \) \(\mathstrut -\mathstrut 28138310036672836977617659816100322616155099852864640775866866896982035999177616032492961297792q^{46} \) \(\mathstrut -\mathstrut 49338615100567586008533951288135845393852650707485360531368204467394665532910688983139358306128q^{47} \) \(\mathstrut +\mathstrut 244064292546444123908052536984208158793401136481260186300744503278739285380247288265778682658816q^{48} \) \(\mathstrut +\mathstrut 752433840599750193271015544145910422089938845099283047668758541087980882087499887025758157789313q^{49} \) \(\mathstrut -\mathstrut 1756648703190643407679915187540746659445068152182448123783254139837888034842840604352884543750000q^{50} \) \(\mathstrut -\mathstrut 4186453060070964308543321243867301742071184523159619262981910395937624269639977914668070815961592q^{51} \) \(\mathstrut -\mathstrut 299921527358232778097628046170322710643014254923572622961503877233695051976123243837021461385728q^{52} \) \(\mathstrut +\mathstrut 45439534345102239290843163912544095765806982832307502313849525819073728936151813167470772365925926q^{53} \) \(\mathstrut +\mathstrut 38680516880674041302480509047884889106404603448054948500904779898349149372610056782201281117946240q^{54} \) \(\mathstrut -\mathstrut 432576867358466335617986215621945887405045763707273014611343529132044150112466209509767824829515000q^{55} \) \(\mathstrut -\mathstrut 159465105485502254328469891445580976480576866382179762995668936857815143816140668281747609575260160q^{56} \) \(\mathstrut +\mathstrut 1990014681911564315630720992224179214491287391034406566984522978256103716439101105615294767535358160q^{57} \) \(\mathstrut +\mathstrut 4618158171946557697639499111957754813666889826993148515766803610504911213619043847144587412863790880q^{58} \) \(\mathstrut -\mathstrut 7994556888742389963754891914386272086617532494092324481666622701281195647537712229818800059078242980q^{59} \) \(\mathstrut -\mathstrut 51547668272403014021235031153713789291688796805654426950141340288411508848106756189101821863952640000q^{60} \) \(\mathstrut -\mathstrut 20010787184525995584720289117304568167948599723976550204852777948468547299349907237396329738847967762q^{61} \) \(\mathstrut +\mathstrut 292035427959193157957119307134870542698832076716753725989233844815905689373991776544712306185499282944q^{62} \) \(\mathstrut +\mathstrut 1084750421819290453616791018398299860321649524662704337157840276934678472457615663242574941575258587176q^{63} \) \(\mathstrut -\mathstrut 2173182954777058552426966649041133062639998025794768537871770595713126062249675532560302339710750031872q^{64} \) \(\mathstrut -\mathstrut 6050492601584073293182223610830486690452314196108303412288731430157341922477676622337759152417832607500q^{65} \) \(\mathstrut -\mathstrut 2811384209515387361103707894564511021023407746835224054361358951726305534503884893008505470528471177984q^{66} \) \(\mathstrut +\mathstrut 24573799368134891916564011470928671317077382485972351268274803174871528123414635568434858147580241074212q^{67} \) \(\mathstrut +\mathstrut 63690775145054712155234191070401247673413728435364958188409307863633237295553890585548320729107243037184q^{68} \) \(\mathstrut -\mathstrut 24003285462463676531332362285165839175525050544235078632804235222118832623175439122841457438544940522656q^{69} \) \(\mathstrut -\mathstrut 863169709419813836575212169649584339603968815833753646438175375944308193587969610263821675032671814880000q^{70} \) \(\mathstrut +\mathstrut 91658679156386468719245489455910792073607873475232020252166152112986794966382882952820365384103518048008q^{71} \) \(\mathstrut +\mathstrut 873882756027094209986251517892994706349418254125301044053004437567652817562627690659257226446504466493440q^{72} \) \(\mathstrut +\mathstrut 541694808507779980546116004112644787310665887489575442433845489271276265038276918082847569639076524144666q^{73} \) \(\mathstrut -\mathstrut 9378706212502591696314586127924566164346165127102664760442762960199173362938872227498081812178947973840224q^{74} \) \(\mathstrut -\mathstrut 29348285812521570443266953567594350343794068770628558899049305240540166160078653563092442717138745889062500q^{75} \) \(\mathstrut -\mathstrut 60564820012723729139203913493989896690950347961424832880261930310236667425867853870924430511072293881605120q^{76} \) \(\mathstrut +\mathstrut 1068940833620544673782151517761484277047755630607342022951044010736792743275783369575718784146165485947744q^{77} \) \(\mathstrut -\mathstrut 286969622560772923408733006352532687901626912195145659167094759389964370273396505496077341678419418050144128q^{78} \) \(\mathstrut -\mathstrut 596276255135400928959400589889218117555952939149585650758445593510201386502571903994653015956197756762453040q^{79} \) \(\mathstrut -\mathstrut 2420836681564557797101060397107174542916086634827557275495079675925079838120631425602247114230349809336320000q^{80} \) \(\mathstrut -\mathstrut 3030606522373897290470630089608148759339991046893156580144516813393469703984963913807719049058860501442725951q^{81} \) \(\mathstrut -\mathstrut 6936458118821589036700513874923262497738432667781968228952468701667638701536840125370171023576003636856609696q^{82} \) \(\mathstrut -\mathstrut 11004287102773590749349691331049602909161139219297045772286679604418555775574362523281340925221936593079346764q^{83} \) \(\mathstrut -\mathstrut 57855325032373861757970130314922242695268575192193159587088758458166711077597077741056893950844377121225826304q^{84} \) \(\mathstrut -\mathstrut 64354197775882201370863569029422599518759619010400232504975477030343845397959668657595763753959731762134552500q^{85} \) \(\mathstrut -\mathstrut 210819753145942403520859363592361681829074054483701088761378978430433240411156075153802810720648226504181908672q^{86} \) \(\mathstrut -\mathstrut 154008309759204716022098762324487951847505839469072421264586325306012373529922474900817730928920322507018969160q^{87} \) \(\mathstrut -\mathstrut 609999238537345062842609214560983373867364799260253404096252032888004927138583268244389069934087697492178288640q^{88} \) \(\mathstrut -\mathstrut 654568028165810774739876366172819409302687924287909841936841472021672950876376689746932135695962343969713322070q^{89} \) \(\mathstrut -\mathstrut 2734380769439054007162335818387627599332566037560181838266985769883367234594498859125630424774118397399333420000q^{90} \) \(\mathstrut -\mathstrut 2323627076132845640660102608242767489368371452521120033992540027246745766005131800187294415915449799674836938512q^{91} \) \(\mathstrut -\mathstrut 4256037231999230829372236189816770749190987971335840398392358871486563229805945773322404171318956972524277721088q^{92} \) \(\mathstrut +\mathstrut 154296866852621529872615733195411660158426537898618117528867810834868770230718469048319703695743778039088292992q^{93} \) \(\mathstrut +\mathstrut 1827384388290191849012043193156273334448650299359011463985703887856827570148696897626054924182121847958990279936q^{94} \) \(\mathstrut -\mathstrut 4096663912916778389991331111354003035604483111168308740332618943380051360421354423075027168404452962459195325000q^{95} \) \(\mathstrut +\mathstrut 8457146062137046129332319587633700387597377410609689871416901579530268721609757152896450994557102813871989587968q^{96} \) \(\mathstrut +\mathstrut 36807391546013154433957869141705553075329468371786108764367006729276625672848917612484272062474831101244619876722q^{97} \) \(\mathstrut +\mathstrut 225562248663489353389248034966442578767140826293081704735030344217680122252159170139356951685061050587472992483824q^{98} \) \(\mathstrut +\mathstrut 321571830004348537474522583988170945954403617464147621640077047560490989900478751999197984675098698758537853855164q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{114}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.114.a.a \(9\) \(80.863\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(49\!\cdots\!32\) \(-1\!\cdots\!24\) \(-3\!\cdots\!50\) \(-1\!\cdots\!08\) \(+\) \(q+(552636039763781+\beta _{1})q^{2}+\cdots\)