## Defining parameters

 Level: $$N$$ = $$187 = 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newforms: $$21$$ Sturm bound: $$5760$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(187))$$.

Total New Old
Modular forms 1600 1541 59
Cusp forms 1281 1269 12
Eisenstein series 319 272 47

## Trace form

 $$1269q - 63q^{2} - 66q^{3} - 75q^{4} - 72q^{5} - 80q^{6} - 68q^{7} - 79q^{8} - 73q^{9} + O(q^{10})$$ $$1269q - 63q^{2} - 66q^{3} - 75q^{4} - 72q^{5} - 80q^{6} - 68q^{7} - 79q^{8} - 73q^{9} - 70q^{10} - 67q^{11} - 120q^{12} - 70q^{13} - 64q^{14} - 38q^{15} - 15q^{16} - 63q^{17} - 111q^{18} - 68q^{19} - 54q^{20} - 52q^{21} - 55q^{22} - 150q^{23} - 44q^{24} - 31q^{25} - 18q^{26} - 66q^{27} - 16q^{28} - 54q^{29} - 12q^{30} - 46q^{31} - 31q^{32} - 34q^{33} - 71q^{34} - 108q^{35} + 13q^{36} - 44q^{37} - 28q^{38} - 16q^{39} + 38q^{40} - 2q^{41} + 40q^{42} - 16q^{43} + 13q^{44} - 114q^{45} - 44q^{46} - 48q^{47} + 12q^{48} - 51q^{49} - 45q^{50} - 70q^{51} - 114q^{52} - 18q^{53} + 76q^{54} - 16q^{55} - 24q^{56} + 48q^{57} + 22q^{58} - 6q^{59} + 108q^{60} - 22q^{61} + 76q^{62} + 64q^{63} + 49q^{64} - 4q^{65} + 40q^{66} - 118q^{67} + 21q^{68} - 2q^{69} + 56q^{70} - 34q^{71} + 133q^{72} + 54q^{73} + 2q^{74} + 60q^{75} + 36q^{76} + 4q^{77} + 8q^{78} + 4q^{79} + 110q^{80} + 21q^{81} - 6q^{82} - 8q^{83} + 72q^{84} + 20q^{85} - 60q^{86} + 8q^{87} + 73q^{88} - 120q^{89} + 150q^{90} + 64q^{91} + 156q^{92} + 14q^{93} + 144q^{94} + 40q^{95} + 228q^{96} - 20q^{97} + 97q^{98} + 71q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$

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
187.2.a $$\chi_{187}(1, \cdot)$$ 187.2.a.a 1 1
187.2.a.b 1
187.2.a.c 2
187.2.a.d 2
187.2.a.e 3
187.2.a.f 4
187.2.d $$\chi_{187}(67, \cdot)$$ 187.2.d.a 16 1
187.2.e $$\chi_{187}(89, \cdot)$$ 187.2.e.a 4 2
187.2.e.b 28
187.2.g $$\chi_{187}(69, \cdot)$$ 187.2.g.a 4 4
187.2.g.b 4
187.2.g.c 4
187.2.g.d 8
187.2.g.e 8
187.2.g.f 36
187.2.h $$\chi_{187}(100, \cdot)$$ 187.2.h.a 56 4
187.2.j $$\chi_{187}(16, \cdot)$$ 187.2.j.a 64 4
187.2.m $$\chi_{187}(10, \cdot)$$ 187.2.m.a 128 8
187.2.p $$\chi_{187}(4, \cdot)$$ 187.2.p.a 128 8
187.2.r $$\chi_{187}(9, \cdot)$$ 187.2.r.a 256 16
187.2.t $$\chi_{187}(6, \cdot)$$ 187.2.t.a 512 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(187))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(187)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$