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Properties

Label 37.9
Level 37
Weight 9
Dimension 438
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 1026
Trace bound 1

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(1026\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(37))\).

Total New Old
Modular forms 474 474 0
Cusp forms 438 438 0
Eisenstein series 36 36 0

Trace form

\( 438 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 438 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} + 4112622 q^{26} - 4251546 q^{27} - 5775378 q^{28} + 1815516 q^{29} + 12690414 q^{30} + 5524452 q^{31} - 3538962 q^{32} - 6593094 q^{33} - 16441362 q^{34} - 8610804 q^{35} + 7943988 q^{37} + 11902428 q^{38} + 14944968 q^{39} + 30965742 q^{40} - 1739088 q^{41} - 25380882 q^{42} - 21715614 q^{43} - 45563922 q^{44} - 17360424 q^{45} + 24007662 q^{46} + 19721376 q^{47} + 79626222 q^{48} - 5294346 q^{49} - 50996754 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} + 151652772 q^{58} - 34515954 q^{59} - 385177356 q^{60} - 82661058 q^{61} + 22806612 q^{62} + 203916942 q^{63} + 318881916 q^{64} + 175092174 q^{65} + 266909058 q^{66} - 13251186 q^{67} - 184195638 q^{68} - 376798482 q^{69} - 572788872 q^{70} - 178092882 q^{71} - 363274326 q^{72} + 225587358 q^{74} + 529068924 q^{75} + 549616446 q^{76} + 285600366 q^{77} + 824144562 q^{78} + 126594990 q^{79} - 73692252 q^{80} - 397168146 q^{81} - 529153902 q^{82} - 223866738 q^{83} - 1550770470 q^{84} - 348096546 q^{85} - 72643680 q^{86} + 487450638 q^{87} + 865705032 q^{88} + 548009262 q^{89} + 1008391464 q^{90} - 15577176 q^{91} - 386942472 q^{92} - 632471724 q^{93} - 1022128146 q^{94} - 635985018 q^{95} - 185633298 q^{96} + 425716182 q^{97} + 1482983406 q^{98} + 1042292772 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(37))\)

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
37.9.d \(\chi_{37}(6, \cdot)\) 37.9.d.a 50 2
37.9.g \(\chi_{37}(8, \cdot)\) 37.9.g.a 100 4
37.9.i \(\chi_{37}(2, \cdot)\) 37.9.i.a 288 12