## 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

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

## 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

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