## Defining parameters

 Level: $$N$$ = $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$45$$ Sturm bound: $$11520$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(285))$$.

Total New Old
Modular forms 3168 2071 1097
Cusp forms 2593 1871 722
Eisenstein series 575 200 375

## Trace form

 $$1871q + 5q^{2} - 15q^{3} - 27q^{4} - q^{5} - 53q^{6} - 28q^{7} + 9q^{8} - 19q^{9} + O(q^{10})$$ $$1871q + 5q^{2} - 15q^{3} - 27q^{4} - q^{5} - 53q^{6} - 28q^{7} + 9q^{8} - 19q^{9} - 49q^{10} + 20q^{11} - 37q^{12} - 66q^{13} - 48q^{14} - 42q^{15} - 219q^{16} - 22q^{17} - 31q^{18} - 105q^{19} - 63q^{20} - 88q^{21} - 116q^{22} - 12q^{23} - 69q^{24} - 91q^{25} - 34q^{26} - 39q^{27} - 136q^{28} - 38q^{29} - 89q^{30} - 148q^{31} - 107q^{32} - 122q^{33} - 158q^{34} - 64q^{35} - 189q^{36} - 86q^{37} - 191q^{38} - 134q^{39} - 207q^{40} - 50q^{41} - 174q^{42} - 144q^{43} - 104q^{44} - 55q^{45} - 216q^{46} - 40q^{47} + 11q^{48} - 37q^{49} - 49q^{50} + 40q^{51} + 58q^{52} + 74q^{53} + 91q^{54} - 34q^{55} + 120q^{56} + 95q^{57} + 14q^{58} + 68q^{59} + 41q^{60} - 162q^{61} - 84q^{62} + 38q^{63} - 211q^{64} - 90q^{65} - 10q^{66} - 280q^{67} - 122q^{68} - 84q^{69} - 246q^{70} - 56q^{71} + 9q^{72} - 306q^{73} - 194q^{74} - 57q^{75} - 331q^{76} - 228q^{77} - 116q^{78} - 220q^{79} + 213q^{80} + 17q^{81} - 286q^{82} + 24q^{83} + 38q^{84} + 32q^{85} + 32q^{86} + 8q^{87} + 240q^{88} - 6q^{89} + 275q^{90} - 44q^{91} + 276q^{92} + 98q^{93} + 376q^{94} + 177q^{95} + 377q^{96} + 166q^{97} + 445q^{98} + 272q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$

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
285.2.a $$\chi_{285}(1, \cdot)$$ 285.2.a.a 1 1
285.2.a.b 1
285.2.a.c 1
285.2.a.d 2
285.2.a.e 2
285.2.a.f 2
285.2.a.g 2
285.2.b $$\chi_{285}(284, \cdot)$$ 285.2.b.a 4 1
285.2.b.b 16
285.2.b.c 16
285.2.c $$\chi_{285}(229, \cdot)$$ 285.2.c.a 6 1
285.2.c.b 14
285.2.h $$\chi_{285}(56, \cdot)$$ 285.2.h.a 28 1
285.2.i $$\chi_{285}(106, \cdot)$$ 285.2.i.a 2 2
285.2.i.b 2
285.2.i.c 2
285.2.i.d 4
285.2.i.e 4
285.2.i.f 10
285.2.k $$\chi_{285}(77, \cdot)$$ 285.2.k.a 4 2
285.2.k.b 4
285.2.k.c 28
285.2.k.d 36
285.2.m $$\chi_{285}(37, \cdot)$$ 285.2.m.a 4 2
285.2.m.b 36
285.2.p $$\chi_{285}(221, \cdot)$$ 285.2.p.a 4 2
285.2.p.b 52
285.2.q $$\chi_{285}(164, \cdot)$$ 285.2.q.a 4 2
285.2.q.b 4
285.2.q.c 8
285.2.q.d 56
285.2.r $$\chi_{285}(49, \cdot)$$ 285.2.r.a 40 2
285.2.u $$\chi_{285}(16, \cdot)$$ 285.2.u.a 12 6
285.2.u.b 18
285.2.u.c 24
285.2.u.d 30
285.2.v $$\chi_{285}(68, \cdot)$$ 285.2.v.a 144 4
285.2.x $$\chi_{285}(88, \cdot)$$ 285.2.x.a 80 4
285.2.z $$\chi_{285}(41, \cdot)$$ 285.2.z.a 156 6
285.2.be $$\chi_{285}(4, \cdot)$$ 285.2.be.a 120 6
285.2.bf $$\chi_{285}(14, \cdot)$$ 285.2.bf.a 12 6
285.2.bf.b 12
285.2.bf.c 192
285.2.bh $$\chi_{285}(13, \cdot)$$ 285.2.bh.a 240 12
285.2.bi $$\chi_{285}(17, \cdot)$$ 285.2.bi.a 432 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(285))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(285)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$