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Properties

Label 37.7
Level 37
Weight 7
Dimension 324
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 798
Trace bound 1

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(798\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(37))\).

Total New Old
Modular forms 360 360 0
Cusp forms 324 324 0
Eisenstein series 36 36 0

Trace form

\( 324 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 324 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} + 146502 q^{26} - 18 q^{27} - 345618 q^{28} - 95778 q^{29} - 139986 q^{30} + 110142 q^{31} + 368622 q^{32} + 233262 q^{33} + 423342 q^{34} + 190926 q^{35} - 166338 q^{37} - 269316 q^{38} - 408258 q^{39} - 1347858 q^{40} - 423378 q^{41} - 233298 q^{42} + 120942 q^{43} + 783342 q^{44} + 944766 q^{45} + 1477422 q^{46} + 293022 q^{47} - 18 q^{48} - 823698 q^{49} - 846234 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} + 2299572 q^{58} + 1311894 q^{59} - 1963980 q^{60} - 1747998 q^{61} - 3796668 q^{62} - 3556458 q^{63} - 2139876 q^{64} + 84870 q^{65} + 4468194 q^{66} + 1104822 q^{67} + 4156362 q^{68} + 5830830 q^{69} + 7283016 q^{70} + 2016414 q^{71} + 3847914 q^{72} - 2323170 q^{74} - 5648796 q^{75} - 6339906 q^{76} - 3777138 q^{77} - 13957038 q^{78} - 3733794 q^{79} - 8206524 q^{80} - 3505554 q^{81} - 160398 q^{82} + 911862 q^{83} + 13435866 q^{84} + 6365610 q^{85} + 12099888 q^{86} + 10712502 q^{87} + 7213032 q^{88} + 1322622 q^{89} - 8098920 q^{90} - 4991562 q^{91} + 6612408 q^{92} + 1799262 q^{93} - 4852242 q^{94} - 8424018 q^{95} - 23184018 q^{96} - 8221842 q^{97} - 11923218 q^{98} - 3833298 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(37))\)

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
37.7.d \(\chi_{37}(6, \cdot)\) 37.7.d.a 36 2
37.7.g \(\chi_{37}(8, \cdot)\) 37.7.g.a 72 4
37.7.i \(\chi_{37}(2, \cdot)\) 37.7.i.a 216 12