Properties

Label 1.36.a
Level 1
Weight 36
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 36 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_0(1))\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

Trace form

\(3q \) \(\mathstrut +\mathstrut 139656q^{2} \) \(\mathstrut -\mathstrut 104875308q^{3} \) \(\mathstrut +\mathstrut 34841262144q^{4} \) \(\mathstrut +\mathstrut 892652054010q^{5} \) \(\mathstrut -\mathstrut 4786530564384q^{6} \) \(\mathstrut +\mathstrut 878422149346056q^{7} \) \(\mathstrut +\mathstrut 22336009925337600q^{8} \) \(\mathstrut +\mathstrut 150091978876243551q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 139656q^{2} \) \(\mathstrut -\mathstrut 104875308q^{3} \) \(\mathstrut +\mathstrut 34841262144q^{4} \) \(\mathstrut +\mathstrut 892652054010q^{5} \) \(\mathstrut -\mathstrut 4786530564384q^{6} \) \(\mathstrut +\mathstrut 878422149346056q^{7} \) \(\mathstrut +\mathstrut 22336009925337600q^{8} \) \(\mathstrut +\mathstrut 150091978876243551q^{9} \) \(\mathstrut +\mathstrut 1019870812729298160q^{10} \) \(\mathstrut -\mathstrut 1157945428549987044q^{11} \) \(\mathstrut -\mathstrut 22548891526776486144q^{12} \) \(\mathstrut -\mathstrut 62139610550998650558q^{13} \) \(\mathstrut +\mathstrut 135909343255071438528q^{14} \) \(\mathstrut +\mathstrut 706062479352366674520q^{15} \) \(\mathstrut +\mathstrut 2155694017285818421248q^{16} \) \(\mathstrut -\mathstrut 3932636930193139724394q^{17} \) \(\mathstrut -\mathstrut 23007400170989698594008q^{18} \) \(\mathstrut -\mathstrut 32303396242934620550940q^{19} \) \(\mathstrut +\mathstrut 147257059647928607018880q^{20} \) \(\mathstrut +\mathstrut 222122458753667398807776q^{21} \) \(\mathstrut +\mathstrut 22658809266113247402912q^{22} \) \(\mathstrut -\mathstrut 514822069421375217224808q^{23} \) \(\mathstrut -\mathstrut 3760729014923614708254720q^{24} \) \(\mathstrut +\mathstrut 646885156836409574920725q^{25} \) \(\mathstrut +\mathstrut 4284481859934908169468336q^{26} \) \(\mathstrut +\mathstrut 27373531144823515220747400q^{27} \) \(\mathstrut +\mathstrut 10448754713452503022622208q^{28} \) \(\mathstrut -\mathstrut 38460399143984437598248110q^{29} \) \(\mathstrut -\mathstrut 234613011392444285921119680q^{30} \) \(\mathstrut +\mathstrut 103731594563724689730029856q^{31} \) \(\mathstrut -\mathstrut 9222369125611166314758144q^{32} \) \(\mathstrut +\mathstrut 1184565114402567148957069584q^{33} \) \(\mathstrut -\mathstrut 554136735348503783026707312q^{34} \) \(\mathstrut +\mathstrut 1596564453000564139676248560q^{35} \) \(\mathstrut -\mathstrut 6052204716130590310531484352q^{36} \) \(\mathstrut +\mathstrut 2464613172948888017021063706q^{37} \) \(\mathstrut -\mathstrut 12543374691225905672793885600q^{38} \) \(\mathstrut +\mathstrut 18611981954062877742706387512q^{39} \) \(\mathstrut +\mathstrut 16458708947711983604007091200q^{40} \) \(\mathstrut +\mathstrut 23522986584532768129037087406q^{41} \) \(\mathstrut -\mathstrut 33931371616975894880367698688q^{42} \) \(\mathstrut -\mathstrut 47516297135443858184325274308q^{43} \) \(\mathstrut -\mathstrut 80954820698705302013923898112q^{44} \) \(\mathstrut -\mathstrut 110576300682246572226345828030q^{45} \) \(\mathstrut +\mathstrut 310121697020384938950505889856q^{46} \) \(\mathstrut +\mathstrut 164346768841318947159729902256q^{47} \) \(\mathstrut +\mathstrut 445342931723856383878644744192q^{48} \) \(\mathstrut -\mathstrut 595089038084925731622037450821q^{49} \) \(\mathstrut +\mathstrut 373669468267473207632799996600q^{50} \) \(\mathstrut -\mathstrut 1803044074850794727352259927704q^{51} \) \(\mathstrut -\mathstrut 511632617456400883939009686144q^{52} \) \(\mathstrut -\mathstrut 1670480551111723484744458809558q^{53} \) \(\mathstrut +\mathstrut 4424231404769003900494105901760q^{54} \) \(\mathstrut +\mathstrut 3067178595313878889174894808520q^{55} \) \(\mathstrut +\mathstrut 5670920217413056567252590243840q^{56} \) \(\mathstrut +\mathstrut 4048712721984947152977307522800q^{57} \) \(\mathstrut -\mathstrut 23757672063982901326871265032400q^{58} \) \(\mathstrut +\mathstrut 4370528583092646699845243631180q^{59} \) \(\mathstrut -\mathstrut 40771862895691439845448715210240q^{60} \) \(\mathstrut +\mathstrut 23537078276516028947219080488306q^{61} \) \(\mathstrut +\mathstrut 29401231764447267309574710842112q^{62} \) \(\mathstrut +\mathstrut 45614247892704690123948892506792q^{63} \) \(\mathstrut +\mathstrut 93510280736634320631093264384q^{64} \) \(\mathstrut +\mathstrut 75762337609865790449417835274620q^{65} \) \(\mathstrut -\mathstrut 75640417841065837797640948042368q^{66} \) \(\mathstrut -\mathstrut 188845033384156918977315211921644q^{67} \) \(\mathstrut +\mathstrut 21990159186015794982823459732608q^{68} \) \(\mathstrut -\mathstrut 325983212396274250308653315934048q^{69} \) \(\mathstrut +\mathstrut 223263426310223328568197933240960q^{70} \) \(\mathstrut +\mathstrut 348774602295358210538621162006856q^{71} \) \(\mathstrut +\mathstrut 314101495165322886769992842611200q^{72} \) \(\mathstrut -\mathstrut 285174964854822786615792218987058q^{73} \) \(\mathstrut +\mathstrut 2106337383176566865790045395789808q^{74} \) \(\mathstrut -\mathstrut 1577819189216049218913461709237300q^{75} \) \(\mathstrut -\mathstrut 2729074287668324197849535448894720q^{76} \) \(\mathstrut +\mathstrut 691501421964810422051915307575712q^{77} \) \(\mathstrut -\mathstrut 2213086042571083132613626950273216q^{78} \) \(\mathstrut -\mathstrut 426212862591061661901736630874160q^{79} \) \(\mathstrut +\mathstrut 6831119561623806264802413342351360q^{80} \) \(\mathstrut +\mathstrut 1867221150796978455595408934723163q^{81} \) \(\mathstrut -\mathstrut 4061181362173286538873115152234288q^{82} \) \(\mathstrut +\mathstrut 14867187331664065317008883105766692q^{83} \) \(\mathstrut -\mathstrut 13024788508690842242825242575869952q^{84} \) \(\mathstrut -\mathstrut 8752040931978292430566755304420140q^{85} \) \(\mathstrut +\mathstrut 148490750656470812540405098190496q^{86} \) \(\mathstrut -\mathstrut 7833119385476156993771606256673800q^{87} \) \(\mathstrut -\mathstrut 18777218849949122679898044025804800q^{88} \) \(\mathstrut +\mathstrut 30583590846193751335205992418034270q^{89} \) \(\mathstrut +\mathstrut 2860720282233327924484406809049520q^{90} \) \(\mathstrut +\mathstrut 1003391702519487362566122156997296q^{91} \) \(\mathstrut +\mathstrut 83662070125024358323030039384121856q^{92} \) \(\mathstrut -\mathstrut 40914650682166972019906140161446016q^{93} \) \(\mathstrut +\mathstrut 19076193270418512575422277142000768q^{94} \) \(\mathstrut -\mathstrut 84521392849966457182141665888160200q^{95} \) \(\mathstrut -\mathstrut 32392027865954425966997293222723584q^{96} \) \(\mathstrut -\mathstrut 106165667044630951063328618701091994q^{97} \) \(\mathstrut -\mathstrut 13202051562017808504422115585262392q^{98} \) \(\mathstrut +\mathstrut 30288686341597731928441860752034252q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.36.a.a \(3\) \(7.760\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(139656\) \(-104875308\) \(892652054010\) \(87\!\cdots\!56\) \(+\) \(q+(46552+\beta _{1})q^{2}+(-34958436+\cdots)q^{3}+\cdots\)