## Defining parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$30$$ Sturm bound: $$13440$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(287))$$.

Total New Old
Modular forms 3600 3411 189
Cusp forms 3121 3019 102
Eisenstein series 479 392 87

## Trace form

 $$3019q - 83q^{2} - 84q^{3} - 87q^{4} - 86q^{5} - 92q^{6} - 101q^{7} - 215q^{8} - 93q^{9} + O(q^{10})$$ $$3019q - 83q^{2} - 84q^{3} - 87q^{4} - 86q^{5} - 92q^{6} - 101q^{7} - 215q^{8} - 93q^{9} - 98q^{10} - 92q^{11} - 108q^{12} - 94q^{13} - 103q^{14} - 224q^{15} - 111q^{16} - 98q^{17} - 119q^{18} - 100q^{19} - 122q^{20} - 104q^{21} - 236q^{22} - 104q^{23} - 140q^{24} - 111q^{25} - 122q^{26} - 120q^{27} - 107q^{28} - 230q^{29} - 72q^{30} - 72q^{31} - 3q^{32} - 8q^{33} - 34q^{34} - 66q^{35} - 11q^{36} + 2q^{37} - 60q^{38} + 24q^{39} + 110q^{40} - 81q^{41} - 52q^{42} - 204q^{43} + 76q^{44} + 2q^{45} - 72q^{46} - 8q^{47} + 76q^{48} - 61q^{49} - 193q^{50} - 32q^{51} - 38q^{52} - 94q^{53} - 120q^{54} - 152q^{55} - 115q^{56} - 280q^{57} - 170q^{58} - 140q^{59} - 248q^{60} - 142q^{61} - 176q^{62} - 113q^{63} - 327q^{64} - 144q^{65} - 64q^{66} - 28q^{67} - 6q^{68} - 16q^{69} + 82q^{70} - 112q^{71} + 85q^{72} + 6q^{73} + 46q^{74} + 116q^{75} + 380q^{76} - 32q^{77} + 32q^{78} + 214q^{80} + 179q^{81} + 277q^{82} - 84q^{83} + 152q^{84} + 32q^{85} + 188q^{86} - 40q^{87} + 140q^{88} - 10q^{89} + 286q^{90} + 46q^{91} - 128q^{92} - 48q^{93} + 136q^{94} - 40q^{95} + 68q^{96} - 18q^{97} - 3q^{98} - 236q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$

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
287.2.a $$\chi_{287}(1, \cdot)$$ 287.2.a.a 2 1
287.2.a.b 2
287.2.a.c 3
287.2.a.d 3
287.2.a.e 5
287.2.a.f 6
287.2.c $$\chi_{287}(204, \cdot)$$ 287.2.c.a 10 1
287.2.c.b 12
287.2.e $$\chi_{287}(165, \cdot)$$ 287.2.e.a 4 2
287.2.e.b 4
287.2.e.c 10
287.2.e.d 34
287.2.f $$\chi_{287}(50, \cdot)$$ 287.2.f.a 40 2
287.2.h $$\chi_{287}(57, \cdot)$$ 287.2.h.a 4 4
287.2.h.b 4
287.2.h.c 40
287.2.h.d 40
287.2.j $$\chi_{287}(81, \cdot)$$ 287.2.j.a 52 2
287.2.l $$\chi_{287}(27, \cdot)$$ 287.2.l.a 104 4
287.2.n $$\chi_{287}(64, \cdot)$$ 287.2.n.a 88 4
287.2.r $$\chi_{287}(9, \cdot)$$ 287.2.r.a 4 4
287.2.r.b 4
287.2.r.c 96
287.2.s $$\chi_{287}(16, \cdot)$$ 287.2.s.a 208 8
287.2.u $$\chi_{287}(8, \cdot)$$ 287.2.u.a 160 8
287.2.w $$\chi_{287}(3, \cdot)$$ 287.2.w.a 208 8
287.2.z $$\chi_{287}(4, \cdot)$$ 287.2.z.a 208 8
287.2.bb $$\chi_{287}(6, \cdot)$$ 287.2.bb.a 416 16
287.2.bc $$\chi_{287}(2, \cdot)$$ 287.2.bc.a 416 16
287.2.be $$\chi_{287}(12, \cdot)$$ 287.2.be.a 832 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(287))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(287)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 2}$$