Properties

Label 1.54.a
Level 1
Weight 54
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 4
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 54 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{54}(\Gamma_0(1))\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 68476320q^{2} \) \(\mathstrut -\mathstrut 1048411007280q^{3} \) \(\mathstrut +\mathstrut 7829639419798528q^{4} \) \(\mathstrut -\mathstrut 4563895793294313000q^{5} \) \(\mathstrut +\mathstrut 365243285516994476928q^{6} \) \(\mathstrut -\mathstrut 224841770748445429600q^{7} \) \(\mathstrut +\mathstrut 139144349902380051824640q^{8} \) \(\mathstrut +\mathstrut 11374560253581116395684212q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 68476320q^{2} \) \(\mathstrut -\mathstrut 1048411007280q^{3} \) \(\mathstrut +\mathstrut 7829639419798528q^{4} \) \(\mathstrut -\mathstrut 4563895793294313000q^{5} \) \(\mathstrut +\mathstrut 365243285516994476928q^{6} \) \(\mathstrut -\mathstrut 224841770748445429600q^{7} \) \(\mathstrut +\mathstrut 139144349902380051824640q^{8} \) \(\mathstrut +\mathstrut 11374560253581116395684212q^{9} \) \(\mathstrut +\mathstrut 239691034935725362703784000q^{10} \) \(\mathstrut +\mathstrut 2482225436399137396212828528q^{11} \) \(\mathstrut -\mathstrut 36954074065409878778429091840q^{12} \) \(\mathstrut +\mathstrut 38846785417115118418757458040q^{13} \) \(\mathstrut -\mathstrut 2318389217831653006768429089024q^{14} \) \(\mathstrut +\mathstrut 10885572770546350531014554412000q^{15} \) \(\mathstrut -\mathstrut 158675761303426594387641091751936q^{16} \) \(\mathstrut -\mathstrut 869470789827683332623267869375160q^{17} \) \(\mathstrut -\mathstrut 6763457530054882037574097250222880q^{18} \) \(\mathstrut -\mathstrut 25573430606481293737377136094590960q^{19} \) \(\mathstrut -\mathstrut 137124186244908431721319713321216000q^{20} \) \(\mathstrut -\mathstrut 456430072728043514442750337944104832q^{21} \) \(\mathstrut -\mathstrut 930239272324579210970924539473171840q^{22} \) \(\mathstrut +\mathstrut 692283403499940921426611559815316960q^{23} \) \(\mathstrut +\mathstrut 8087484160806183674287697801240248320q^{24} \) \(\mathstrut +\mathstrut 36481255519181820020535795184467437500q^{25} \) \(\mathstrut +\mathstrut 88199592302469577023283184091414497088q^{26} \) \(\mathstrut +\mathstrut 85289145712610214901983766257673297440q^{27} \) \(\mathstrut -\mathstrut 5693966184427848677134093343909109760q^{28} \) \(\mathstrut -\mathstrut 1403448065249545071892827367228561632840q^{29} \) \(\mathstrut -\mathstrut 5799093432823921615312476874120821216000q^{30} \) \(\mathstrut -\mathstrut 3964172885133396823441211087460727887232q^{31} \) \(\mathstrut +\mathstrut 3478175004061909463146496356345215713280q^{32} \) \(\mathstrut +\mathstrut 26488618539649572306469337360654123586240q^{33} \) \(\mathstrut +\mathstrut 149997773608319010417738024908146242937536q^{34} \) \(\mathstrut +\mathstrut 61365948170559642529868826584708753304000q^{35} \) \(\mathstrut +\mathstrut 74373890656883085418751005021443502838784q^{36} \) \(\mathstrut -\mathstrut 283737807523680188930907412534612515795880q^{37} \) \(\mathstrut -\mathstrut 2149858349100743242412726210681586741479040q^{38} \) \(\mathstrut -\mathstrut 3695759405159081384443679869760359201600416q^{39} \) \(\mathstrut -\mathstrut 530824655589569872286083924732862423040000q^{40} \) \(\mathstrut +\mathstrut 816268439352205816307560932682632884757288q^{41} \) \(\mathstrut +\mathstrut 34473336675516302350057635130637873086909440q^{42} \) \(\mathstrut +\mathstrut 45680017888765970285202819125021276867644400q^{43} \) \(\mathstrut +\mathstrut 36450257868828743991533939202628376274333696q^{44} \) \(\mathstrut -\mathstrut 52785302554790432865174172783106255610789000q^{45} \) \(\mathstrut -\mathstrut 286598377899888278123152881845505043619242752q^{46} \) \(\mathstrut -\mathstrut 450331332464449690190061856166374876708223040q^{47} \) \(\mathstrut -\mathstrut 307327868606734954261884348178650744005591040q^{48} \) \(\mathstrut +\mathstrut 61256589204322440136838991964906594854806628q^{49} \) \(\mathstrut +\mathstrut 521470775015683964723409941128468604170500000q^{50} \) \(\mathstrut +\mathstrut 4823104417223604238685131462744139603812556448q^{51} \) \(\mathstrut +\mathstrut 6480873745173555872757727943119261362842777600q^{52} \) \(\mathstrut +\mathstrut 3894630980633224571473003534722579109607488920q^{53} \) \(\mathstrut -\mathstrut 9094643349894867160783307676594158361928776960q^{54} \) \(\mathstrut -\mathstrut 25220087960941681699071033843031097345513916000q^{55} \) \(\mathstrut -\mathstrut 41708301235969326798480993683317763265335132160q^{56} \) \(\mathstrut -\mathstrut 78794438935790744156133212572387836678302205120q^{57} \) \(\mathstrut +\mathstrut 23153390818000102952173078969301145284748805440q^{58} \) \(\mathstrut +\mathstrut 161352440713620380366889082872890081870684067120q^{59} \) \(\mathstrut +\mathstrut 406305479737925709888509415210821103661353984000q^{60} \) \(\mathstrut +\mathstrut 65647964430669998286897420448040378258467279928q^{61} \) \(\mathstrut +\mathstrut 397783228528983419561799088374192602352940661760q^{62} \) \(\mathstrut -\mathstrut 302986559547633524951279897150694105228921738720q^{63} \) \(\mathstrut -\mathstrut 1033735951572319175631379922707833053066697900032q^{64} \) \(\mathstrut -\mathstrut 3420620126550512806970332375686936386825214798000q^{65} \) \(\mathstrut -\mathstrut 658347942888276364671353073747068107649649237504q^{66} \) \(\mathstrut -\mathstrut 1114206317023626852397290701407230552884994982960q^{67} \) \(\mathstrut +\mathstrut 2848472333882807118405541680155589548651324344320q^{68} \) \(\mathstrut +\mathstrut 775291276168249766930956334518267852448076104064q^{69} \) \(\mathstrut +\mathstrut 33179725699094578918821931009364962909309028928000q^{70} \) \(\mathstrut +\mathstrut 3568565136657140046536067623675232742954247775648q^{71} \) \(\mathstrut +\mathstrut 26402495617891679740981292232213348882933665464320q^{72} \) \(\mathstrut -\mathstrut 70697396612705842206652346649767546611106446705240q^{73} \) \(\mathstrut -\mathstrut 2477665041456578897595255396512213772982320606144q^{74} \) \(\mathstrut -\mathstrut 214147644415917420957952976584023331338227237250000q^{75} \) \(\mathstrut +\mathstrut 45189859364823457604586927205450004182295006842880q^{76} \) \(\mathstrut -\mathstrut 161023821416166064076421008340115759390173471196800q^{77} \) \(\mathstrut +\mathstrut 512081797195935502825354508308769411884974336211200q^{78} \) \(\mathstrut -\mathstrut 156417020870005797258130007144678737115075518344640q^{79} \) \(\mathstrut +\mathstrut 1135588155590291950317639086884448883835074772992000q^{80} \) \(\mathstrut -\mathstrut 498743339483968532647094896032944674900788125971356q^{81} \) \(\mathstrut +\mathstrut 1595344511843776298585510858680959074676233895092160q^{82} \) \(\mathstrut -\mathstrut 2616078236644862619515249170129703738064518568891120q^{83} \) \(\mathstrut -\mathstrut 769036580140824400081375315496419857132807898497024q^{84} \) \(\mathstrut -\mathstrut 2322985242765977498040783878693923846942012787106000q^{85} \) \(\mathstrut -\mathstrut 771473689440649042704510533443081756253708267624832q^{86} \) \(\mathstrut -\mathstrut 4553516071908987502170780484180858967295593004331680q^{87} \) \(\mathstrut +\mathstrut 5676678682320308097974311975312643702936459537940480q^{88} \) \(\mathstrut -\mathstrut 377838445322199523132380916699165405584669879895320q^{89} \) \(\mathstrut +\mathstrut 20963916598038401334962666668658272688885372614152000q^{90} \) \(\mathstrut +\mathstrut 12668228612190081366491587480915595422042752342094528q^{91} \) \(\mathstrut +\mathstrut 8910978937854086377493208678167975007758313267978240q^{92} \) \(\mathstrut -\mathstrut 9941509412818307372855389204673554966584205049372160q^{93} \) \(\mathstrut -\mathstrut 37159704993639903541096652460057479885138542709712384q^{94} \) \(\mathstrut -\mathstrut 17088387525725080516970439013001314242158750454180000q^{95} \) \(\mathstrut -\mathstrut 115890361493294838169648124263288994270902966699425792q^{96} \) \(\mathstrut +\mathstrut 10362822344952442405677621761316902058987153293434760q^{97} \) \(\mathstrut -\mathstrut 88214006056362955165305640276151180685109758813947040q^{98} \) \(\mathstrut +\mathstrut 200357011548750056817277275156798035565052172823063984q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{54}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.54.a.a \(4\) \(17.790\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-68476320\) \(-1\!\cdots\!80\) \(-4\!\cdots\!00\) \(-2\!\cdots\!00\) \(+\) \(q+(-17119080+\beta _{1})q^{2}+(-262102751820+\cdots)q^{3}+\cdots\)