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Properties

Label 37.11
Level 37
Weight 11
Dimension 552
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 1254
Trace bound 1

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(1254\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(37))\).

Total New Old
Modular forms 588 588 0
Cusp forms 552 552 0
Eisenstein series 36 36 0

Trace form

\( 552 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 552 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} + 98359182 q^{26} - 114791274 q^{27} + 224747502 q^{28} + 64194336 q^{29} - 178599186 q^{30} - 310269168 q^{31} - 207618066 q^{32} + 121763394 q^{33} + 562841838 q^{34} + 360237816 q^{35} - 352220376 q^{37} - 468137124 q^{38} - 410271012 q^{39} + 174735342 q^{40} + 810795132 q^{41} + 1629787374 q^{42} + 579821994 q^{43} - 423051282 q^{44} - 1756943964 q^{45} - 2934201618 q^{46} - 114847740 q^{47} + 3822059502 q^{48} + 1601758374 q^{49} - 2780146674 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} + 8794333332 q^{58} - 7259008698 q^{59} - 11803426380 q^{60} + 4685690682 q^{61} + 14525902692 q^{62} + 8813669382 q^{63} - 6222592548 q^{64} - 11914736490 q^{65} - 41616984798 q^{66} - 3661012314 q^{67} + 1226612682 q^{68} + 18208745262 q^{69} + 39348473256 q^{70} + 14411981502 q^{71} + 32007195882 q^{72} - 20439763938 q^{74} - 45469793196 q^{75} - 41983292610 q^{76} - 17018308530 q^{77} - 23048430318 q^{78} + 7857905022 q^{79} + 60701476356 q^{80} + 61922298222 q^{81} + 44998167474 q^{82} + 8493262182 q^{83} - 21917386278 q^{84} - 36941152590 q^{85} - 89272973808 q^{86} - 70359149466 q^{87} - 13438311768 q^{88} + 32268092382 q^{89} + 175515777720 q^{90} + 50810004948 q^{91} - 142394272200 q^{92} - 80706558456 q^{93} - 26630461458 q^{94} + 53767124982 q^{95} + 212921210862 q^{96} + 66716236998 q^{97} + 37395274734 q^{98} - 42686567568 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(37))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
37.11.d \(\chi_{37}(6, \cdot)\) 37.11.d.a 60 2
37.11.g \(\chi_{37}(8, \cdot)\) 37.11.g.a 120 4
37.11.i \(\chi_{37}(2, \cdot)\) 37.11.i.a 372 12