## Defining parameters

 Level: $$N$$ = $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$41$$ Sturm bound: $$101376$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(920))$$.

Total New Old
Modular forms 26400 13270 13130
Cusp forms 24289 12766 11523
Eisenstein series 2111 504 1607

## Trace form

 $$12766 q - 36 q^{2} - 36 q^{3} - 36 q^{4} + 2 q^{5} - 116 q^{6} - 28 q^{7} - 36 q^{8} - 62 q^{9} + O(q^{10})$$ $$12766 q - 36 q^{2} - 36 q^{3} - 36 q^{4} + 2 q^{5} - 116 q^{6} - 28 q^{7} - 36 q^{8} - 62 q^{9} - 58 q^{10} - 108 q^{11} - 60 q^{12} + 4 q^{13} - 60 q^{14} - 74 q^{15} - 148 q^{16} - 76 q^{17} - 92 q^{18} - 68 q^{19} - 98 q^{20} - 16 q^{21} - 76 q^{22} - 44 q^{23} - 136 q^{24} - 106 q^{25} - 148 q^{26} - 60 q^{27} - 28 q^{28} + 12 q^{29} - 66 q^{30} - 132 q^{31} + 4 q^{32} - 72 q^{33} + 28 q^{34} - 60 q^{35} - 52 q^{36} + 76 q^{37} + 4 q^{38} + 28 q^{39} + 22 q^{40} - 184 q^{41} + 4 q^{42} + 4 q^{43} - 12 q^{44} + 68 q^{45} - 100 q^{46} - 48 q^{47} - 28 q^{48} + 30 q^{49} - 98 q^{50} - 60 q^{51} - 84 q^{52} + 32 q^{53} - 92 q^{54} - 78 q^{55} - 228 q^{56} - 32 q^{57} - 132 q^{58} - 40 q^{59} - 146 q^{60} + 44 q^{61} - 156 q^{62} - 28 q^{63} - 108 q^{64} - 160 q^{65} - 296 q^{66} - 4 q^{67} - 84 q^{68} - 8 q^{69} - 132 q^{70} - 84 q^{71} - 20 q^{72} - 140 q^{73} - 48 q^{74} + 20 q^{75} - 352 q^{76} + 32 q^{77} - 356 q^{78} - 16 q^{79} - 216 q^{80} - 534 q^{81} - 236 q^{82} - 56 q^{83} - 596 q^{84} - 70 q^{85} - 588 q^{86} - 344 q^{87} - 396 q^{88} - 248 q^{89} - 476 q^{90} - 408 q^{91} - 424 q^{92} - 504 q^{94} - 174 q^{95} - 1064 q^{96} - 192 q^{97} - 420 q^{98} - 432 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$

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
920.2.a $$\chi_{920}(1, \cdot)$$ 920.2.a.a 1 1
920.2.a.b 1
920.2.a.c 1
920.2.a.d 1
920.2.a.e 2
920.2.a.f 2
920.2.a.g 3
920.2.a.h 3
920.2.a.i 3
920.2.a.j 5
920.2.b $$\chi_{920}(459, \cdot)$$ 920.2.b.a 4 1
920.2.b.b 136
920.2.e $$\chi_{920}(369, \cdot)$$ 920.2.e.a 2 1
920.2.e.b 14
920.2.e.c 16
920.2.f $$\chi_{920}(461, \cdot)$$ 920.2.f.a 2 1
920.2.f.b 8
920.2.f.c 30
920.2.f.d 48
920.2.i $$\chi_{920}(551, \cdot)$$ None 0 1
920.2.j $$\chi_{920}(829, \cdot)$$ 920.2.j.a 132 1
920.2.m $$\chi_{920}(919, \cdot)$$ None 0 1
920.2.n $$\chi_{920}(91, \cdot)$$ 920.2.n.a 48 1
920.2.n.b 48
920.2.q $$\chi_{920}(137, \cdot)$$ 920.2.q.a 72 2
920.2.s $$\chi_{920}(47, \cdot)$$ None 0 2
920.2.v $$\chi_{920}(323, \cdot)$$ 920.2.v.a 264 2
920.2.x $$\chi_{920}(413, \cdot)$$ 920.2.x.a 8 2
920.2.x.b 8
920.2.x.c 264
920.2.y $$\chi_{920}(41, \cdot)$$ 920.2.y.a 50 10
920.2.y.b 60
920.2.y.c 60
920.2.y.d 70
920.2.bb $$\chi_{920}(11, \cdot)$$ 920.2.bb.a 480 10
920.2.bb.b 480
920.2.bc $$\chi_{920}(79, \cdot)$$ None 0 10
920.2.bf $$\chi_{920}(29, \cdot)$$ 920.2.bf.a 1400 10
920.2.bg $$\chi_{920}(111, \cdot)$$ None 0 10
920.2.bj $$\chi_{920}(101, \cdot)$$ 920.2.bj.a 960 10
920.2.bk $$\chi_{920}(9, \cdot)$$ 920.2.bk.a 360 10
920.2.bn $$\chi_{920}(19, \cdot)$$ 920.2.bn.a 40 10
920.2.bn.b 1360
920.2.bo $$\chi_{920}(37, \cdot)$$ 920.2.bo.a 2800 20
920.2.bq $$\chi_{920}(3, \cdot)$$ 920.2.bq.a 2800 20
920.2.bt $$\chi_{920}(87, \cdot)$$ None 0 20
920.2.bv $$\chi_{920}(17, \cdot)$$ 920.2.bv.a 720 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(920))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(920)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 2}$$