Properties

Label 37.2
Level 37
Weight 2
Dimension 40
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 228
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(228\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(37))\).

Total New Old
Modular forms 75 75 0
Cusp forms 40 40 0
Eisenstein series 35 35 0

Trace form

\( 40q - 15q^{2} - 14q^{3} - 11q^{4} - 12q^{5} - 6q^{6} - 10q^{7} - 3q^{8} - 5q^{9} + O(q^{10}) \) \( 40q - 15q^{2} - 14q^{3} - 11q^{4} - 12q^{5} - 6q^{6} - 10q^{7} - 3q^{8} - 5q^{9} - 6q^{11} + 10q^{12} - 4q^{13} + 6q^{14} + 6q^{15} + 13q^{16} + 21q^{18} + 2q^{19} + 24q^{20} + 14q^{21} + 18q^{22} + 6q^{23} + 42q^{24} + 13q^{25} + 15q^{26} - 2q^{27} - 22q^{28} - 6q^{29} - 18q^{30} - 40q^{31} - 27q^{32} - 6q^{33} - 36q^{34} - 24q^{35} - 80q^{36} - 23q^{37} - 12q^{38} - 4q^{39} - 63q^{40} - 30q^{41} + 6q^{42} - 10q^{43} - 6q^{44} + 6q^{45} - 18q^{46} + 12q^{47} + 46q^{48} + 15q^{49} + 66q^{50} + 54q^{51} + 80q^{52} + 36q^{53} + 102q^{54} + 54q^{55} + 102q^{56} + 62q^{57} + 54q^{58} + 6q^{59} + 24q^{60} - q^{61} - 12q^{62} - 22q^{63} - 17q^{64} - 15q^{65} - 126q^{66} + 14q^{67} - 66q^{69} - 72q^{70} - 18q^{71} - 111q^{72} - 34q^{73} - 51q^{74} - 92q^{75} - 58q^{76} + 6q^{77} - 102q^{78} - 10q^{79} - 30q^{80} - 41q^{81} + 30q^{83} - 46q^{84} + 9q^{85} - 12q^{86} - 6q^{87} + 72q^{88} + 27q^{89} + 90q^{90} + 52q^{91} + 60q^{92} + 56q^{93} + 54q^{94} + 30q^{95} + 54q^{96} + 8q^{97} + 9q^{98} + 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
37.2.a \(\chi_{37}(1, \cdot)\) 37.2.a.a 1 1
37.2.a.b 1
37.2.b \(\chi_{37}(36, \cdot)\) 37.2.b.a 2 1
37.2.c \(\chi_{37}(10, \cdot)\) 37.2.c.a 2 2
37.2.e \(\chi_{37}(11, \cdot)\) 37.2.e.a 4 2
37.2.f \(\chi_{37}(7, \cdot)\) 37.2.f.a 6 6
37.2.f.b 6
37.2.h \(\chi_{37}(3, \cdot)\) 37.2.h.a 18 6