## Defining parameters

 Level: $$N$$ = $$185 = 5 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$31$$ Sturm bound: $$5472$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(185))$$.

Total New Old
Modular forms 1512 1357 155
Cusp forms 1225 1145 80
Eisenstein series 287 212 75

## Trace form

 $$1145q - 39q^{2} - 40q^{3} - 43q^{4} - 55q^{5} - 120q^{6} - 44q^{7} - 51q^{8} - 49q^{9} + O(q^{10})$$ $$1145q - 39q^{2} - 40q^{3} - 43q^{4} - 55q^{5} - 120q^{6} - 44q^{7} - 51q^{8} - 49q^{9} - 57q^{10} - 120q^{11} - 64q^{12} - 50q^{13} - 60q^{14} - 58q^{15} - 139q^{16} - 54q^{17} - 75q^{18} - 56q^{19} - 61q^{20} - 140q^{21} - 72q^{22} - 60q^{23} - 96q^{24} - 55q^{25} - 132q^{26} - 28q^{27} + 28q^{28} - 30q^{29} + 6q^{30} - 32q^{31} + 45q^{32} - 12q^{33} + 54q^{34} - 8q^{35} + 107q^{36} + 11q^{37} - 60q^{38} - 8q^{39} + 66q^{40} - 42q^{41} + 12q^{42} - 8q^{43} + 24q^{44} - 13q^{45} - 36q^{46} - 48q^{47} - 40q^{48} - 45q^{49} - 48q^{50} - 180q^{51} - 134q^{52} - 90q^{53} - 156q^{54} - 66q^{55} - 228q^{56} - 116q^{57} - 90q^{58} - 24q^{59} + 44q^{60} - 80q^{61} + 48q^{62} + 76q^{63} + 89q^{64} + 13q^{65} + 252q^{66} - 32q^{67} + 54q^{68} + 156q^{69} + 120q^{70} - 36q^{71} + 345q^{72} + 70q^{73} + 141q^{74} + 68q^{75} + 112q^{76} + 12q^{77} + 300q^{78} + 28q^{79} + 113q^{80} + 59q^{81} + 54q^{82} - 48q^{83} + 244q^{84} + 9q^{85} + 12q^{86} + 60q^{87} - 36q^{88} - 36q^{89} + 33q^{90} - 136q^{91} - 24q^{92} - 56q^{93} - 36q^{94} - 2q^{95} + 10q^{97} + 81q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$

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
185.2.a $$\chi_{185}(1, \cdot)$$ 185.2.a.a 1 1
185.2.a.b 1
185.2.a.c 1
185.2.a.d 5
185.2.a.e 5
185.2.b $$\chi_{185}(149, \cdot)$$ 185.2.b.a 18 1
185.2.c $$\chi_{185}(36, \cdot)$$ 185.2.c.a 2 1
185.2.c.b 12
185.2.d $$\chi_{185}(184, \cdot)$$ 185.2.d.a 16 1
185.2.e $$\chi_{185}(26, \cdot)$$ 185.2.e.a 14 2
185.2.e.b 14
185.2.f $$\chi_{185}(43, \cdot)$$ 185.2.f.a 2 2
185.2.f.b 2
185.2.f.c 6
185.2.f.d 24
185.2.k $$\chi_{185}(68, \cdot)$$ 185.2.k.a 2 2
185.2.k.b 2
185.2.k.c 6
185.2.k.d 24
185.2.l $$\chi_{185}(64, \cdot)$$ 185.2.l.a 32 2
185.2.m $$\chi_{185}(11, \cdot)$$ 185.2.m.a 28 2
185.2.n $$\chi_{185}(84, \cdot)$$ 185.2.n.a 36 2
185.2.o $$\chi_{185}(16, \cdot)$$ 185.2.o.a 36 6
185.2.o.b 36
185.2.p $$\chi_{185}(82, \cdot)$$ 185.2.p.a 68 4
185.2.u $$\chi_{185}(8, \cdot)$$ 185.2.u.a 68 4
185.2.v $$\chi_{185}(4, \cdot)$$ 185.2.v.a 96 6
185.2.w $$\chi_{185}(21, \cdot)$$ 185.2.w.a 72 6
185.2.x $$\chi_{185}(9, \cdot)$$ 185.2.x.a 108 6
185.2.z $$\chi_{185}(17, \cdot)$$ 185.2.z.a 204 12
185.2.bc $$\chi_{185}(2, \cdot)$$ 185.2.bc.a 204 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(185))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(185)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 2}$$