## Defining parameters

 Level: $$N$$ = $$74 = 2 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$684$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(74))$$.

Total New Old
Modular forms 207 56 151
Cusp forms 136 56 80
Eisenstein series 71 0 71

## Trace form

 $$56q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$56q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 32q^{21} - 12q^{22} - 24q^{23} - 4q^{24} - 31q^{25} - 5q^{26} + 8q^{27} + 4q^{28} + 6q^{29} + 48q^{30} + 76q^{31} - q^{32} + 24q^{33} + 54q^{34} + 60q^{35} + 32q^{36} + 47q^{37} + 16q^{38} + 28q^{39} + 39q^{40} + 66q^{41} + 40q^{42} + 28q^{43} - 12q^{44} + 30q^{45} + 48q^{46} - 12q^{47} + 8q^{48} - 9q^{49} - 22q^{50} - 72q^{51} - 14q^{52} - 54q^{53} - 40q^{54} - 72q^{55} - 8q^{56} - 80q^{57} - 30q^{58} - 24q^{59} - 24q^{60} - 17q^{61} - 32q^{62} + 4q^{63} - q^{64} - 3q^{65} - 48q^{66} - 32q^{67} - 18q^{68} + 48q^{69} - 48q^{70} - 13q^{72} - 2q^{73} - 37q^{74} + 56q^{75} - 20q^{76} - 24q^{77} - 56q^{78} - 8q^{79} - 6q^{80} + 23q^{81} - 42q^{82} - 48q^{83} - 32q^{84} - 27q^{85} - 44q^{86} - 12q^{87} - 12q^{88} - 45q^{89} - 78q^{90} - 64q^{91} + 12q^{92} - 20q^{93} + 24q^{94} + 24q^{95} - 4q^{96} + 46q^{97} + 87q^{98} + 24q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$

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
74.2.a $$\chi_{74}(1, \cdot)$$ 74.2.a.a 2 1
74.2.a.b 2
74.2.b $$\chi_{74}(73, \cdot)$$ 74.2.b.a 4 1
74.2.c $$\chi_{74}(47, \cdot)$$ 74.2.c.a 2 2
74.2.c.b 2
74.2.c.c 6
74.2.e $$\chi_{74}(11, \cdot)$$ 74.2.e.a 4 2
74.2.e.b 4
74.2.f $$\chi_{74}(7, \cdot)$$ 74.2.f.a 6 6
74.2.f.b 12
74.2.h $$\chi_{74}(3, \cdot)$$ 74.2.h.a 12 6

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(74))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(74)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 2}$$