Properties

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

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 8 \)
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

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

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