## 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

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

## 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