## 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