# Properties

 Label 476.2 Level 476 Weight 2 Dimension 3688 Nonzero newspaces 20 Newform subspaces 30 Sturm bound 27648 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$476 = 2^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$30$$ Sturm bound: $$27648$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(476))$$.

Total New Old
Modular forms 7392 3984 3408
Cusp forms 6433 3688 2745
Eisenstein series 959 296 663

## Trace form

 $$3688 q - 26 q^{2} + 2 q^{3} - 26 q^{4} - 46 q^{5} - 32 q^{6} + 8 q^{7} - 74 q^{8} - 56 q^{9} + O(q^{10})$$ $$3688 q - 26 q^{2} + 2 q^{3} - 26 q^{4} - 46 q^{5} - 32 q^{6} + 8 q^{7} - 74 q^{8} - 56 q^{9} - 44 q^{10} + 10 q^{11} - 56 q^{12} - 56 q^{13} - 58 q^{14} + 36 q^{15} - 66 q^{16} - 39 q^{17} - 70 q^{18} + 14 q^{19} - 32 q^{20} - 66 q^{21} - 44 q^{22} + 22 q^{23} - 40 q^{24} - 92 q^{25} - 72 q^{26} - 28 q^{27} - 34 q^{28} - 200 q^{29} - 148 q^{30} - 78 q^{31} - 106 q^{32} - 178 q^{33} - 160 q^{34} - 62 q^{35} - 226 q^{36} - 142 q^{37} - 148 q^{38} - 28 q^{39} - 184 q^{40} - 80 q^{41} - 112 q^{42} - 132 q^{44} - 52 q^{45} - 88 q^{46} + 62 q^{47} + 16 q^{48} - 16 q^{49} - 102 q^{50} + 67 q^{51} - 64 q^{52} + 18 q^{53} + 36 q^{54} + 68 q^{55} - 18 q^{56} - 180 q^{57} + 92 q^{58} + 50 q^{59} + 200 q^{60} - 94 q^{61} + 80 q^{62} - 4 q^{63} - 2 q^{64} - 260 q^{65} + 156 q^{66} - 46 q^{67} + 144 q^{68} - 300 q^{69} + 20 q^{70} + 206 q^{72} - 262 q^{73} + 88 q^{74} - 24 q^{75} + 80 q^{76} - 138 q^{77} + 80 q^{78} + 6 q^{79} + 48 q^{80} - 214 q^{81} + 24 q^{82} - 48 q^{83} - 48 q^{84} - 182 q^{85} - 188 q^{86} - 12 q^{87} - 196 q^{88} - 190 q^{89} - 192 q^{90} - 292 q^{92} - 154 q^{93} - 164 q^{94} - 102 q^{95} - 288 q^{96} - 24 q^{97} - 146 q^{98} - 152 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$

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
476.2.a $$\chi_{476}(1, \cdot)$$ 476.2.a.a 2 1
476.2.a.b 2
476.2.a.c 2
476.2.a.d 2
476.2.b $$\chi_{476}(169, \cdot)$$ 476.2.b.a 8 1
476.2.e $$\chi_{476}(475, \cdot)$$ 476.2.e.a 8 1
476.2.e.b 20
476.2.e.c 40
476.2.f $$\chi_{476}(307, \cdot)$$ 476.2.f.a 64 1
476.2.i $$\chi_{476}(137, \cdot)$$ 476.2.i.a 2 2
476.2.i.b 2
476.2.i.c 2
476.2.i.d 6
476.2.i.e 8
476.2.k $$\chi_{476}(55, \cdot)$$ 476.2.k.a 136 2
476.2.l $$\chi_{476}(225, \cdot)$$ 476.2.l.a 16 2
476.2.p $$\chi_{476}(103, \cdot)$$ 476.2.p.a 128 2
476.2.q $$\chi_{476}(271, \cdot)$$ 476.2.q.a 16 2
476.2.q.b 120
476.2.t $$\chi_{476}(305, \cdot)$$ 476.2.t.a 24 2
476.2.u $$\chi_{476}(253, \cdot)$$ 476.2.u.a 40 4
476.2.w $$\chi_{476}(83, \cdot)$$ 476.2.w.a 272 4
476.2.z $$\chi_{476}(47, \cdot)$$ 476.2.z.a 272 4
476.2.ba $$\chi_{476}(81, \cdot)$$ 476.2.ba.a 48 4
476.2.bd $$\chi_{476}(71, \cdot)$$ 476.2.bd.a 432 8
476.2.be $$\chi_{476}(41, \cdot)$$ 476.2.be.a 96 8
476.2.bh $$\chi_{476}(9, \cdot)$$ 476.2.bh.a 96 8
476.2.bj $$\chi_{476}(19, \cdot)$$ 476.2.bj.a 544 8
476.2.bl $$\chi_{476}(5, \cdot)$$ 476.2.bl.a 192 16
476.2.bm $$\chi_{476}(11, \cdot)$$ 476.2.bm.a 1088 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(476))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(476)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 2}$$