## Defining parameters

 Level: $$N$$ = $$1476 = 2^{2} \cdot 3^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$241920$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1476))$$.

Total New Old
Modular forms 62080 28248 33832
Cusp forms 58881 27544 31337
Eisenstein series 3199 704 2495

## Trace form

 $$27544q - 54q^{2} - 50q^{4} - 102q^{5} - 74q^{6} + 6q^{7} - 60q^{8} - 136q^{9} + O(q^{10})$$ $$27544q - 54q^{2} - 50q^{4} - 102q^{5} - 74q^{6} + 6q^{7} - 60q^{8} - 136q^{9} - 172q^{10} + 6q^{11} - 92q^{12} - 106q^{13} - 84q^{14} - 18q^{15} - 74q^{16} - 144q^{17} - 116q^{18} - 96q^{20} - 154q^{21} - 66q^{22} - 6q^{23} - 86q^{24} - 102q^{25} - 60q^{26} - 156q^{28} - 126q^{29} - 44q^{30} - 2q^{31} + 6q^{32} - 190q^{33} - 34q^{34} - 28q^{35} - 14q^{36} - 400q^{37} - 6q^{38} + 6q^{39} - 44q^{40} - 161q^{41} - 124q^{42} - 38q^{43} - 60q^{44} - 190q^{45} - 204q^{46} - 78q^{47} - 122q^{48} - 198q^{49} - 102q^{50} - 124q^{52} - 116q^{53} - 158q^{54} - 36q^{55} - 96q^{56} - 172q^{57} - 124q^{58} - 6q^{59} - 92q^{60} - 130q^{61} - 60q^{62} + 6q^{63} - 200q^{64} - 56q^{65} - 32q^{66} + 78q^{67} + 70q^{68} - 82q^{69} + 152q^{70} + 128q^{71} - 38q^{72} - 164q^{73} + 120q^{74} + 24q^{75} + 246q^{76} + 14q^{77} - 56q^{78} + 110q^{79} + 140q^{80} - 136q^{81} + 46q^{82} + 62q^{83} - 140q^{84} + 30q^{85} + 98q^{86} + 18q^{87} + 182q^{88} - 64q^{89} - 92q^{90} + 172q^{91} + 12q^{92} - 250q^{93} + 156q^{94} + 56q^{95} - 104q^{96} - 86q^{97} + 40q^{98} - 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1476))$$

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
1476.2.a $$\chi_{1476}(1, \cdot)$$ 1476.2.a.a 1 1
1476.2.a.b 1
1476.2.a.c 2
1476.2.a.d 2
1476.2.a.e 3
1476.2.a.f 3
1476.2.a.g 4
1476.2.c $$\chi_{1476}(575, \cdot)$$ 1476.2.c.a 80 1
1476.2.d $$\chi_{1476}(1475, \cdot)$$ 1476.2.d.a 4 1
1476.2.d.b 8
1476.2.d.c 8
1476.2.d.d 64
1476.2.f $$\chi_{1476}(901, \cdot)$$ 1476.2.f.a 2 1
1476.2.f.b 2
1476.2.f.c 4
1476.2.f.d 4
1476.2.f.e 6
1476.2.i $$\chi_{1476}(493, \cdot)$$ 1476.2.i.a 2 2
1476.2.i.b 32
1476.2.i.c 46
1476.2.k $$\chi_{1476}(73, \cdot)$$ 1476.2.k.a 6 2
1476.2.k.b 12
1476.2.k.c 16
1476.2.m $$\chi_{1476}(647, \cdot)$$ n/a 168 2
1476.2.n $$\chi_{1476}(37, \cdot)$$ 1476.2.n.a 4 4
1476.2.n.b 4
1476.2.n.c 4
1476.2.n.d 4
1476.2.n.e 8
1476.2.n.f 16
1476.2.n.g 32
1476.2.q $$\chi_{1476}(409, \cdot)$$ 1476.2.q.a 8 2
1476.2.q.b 76
1476.2.s $$\chi_{1476}(491, \cdot)$$ n/a 496 2
1476.2.t $$\chi_{1476}(83, \cdot)$$ n/a 480 2
1476.2.x $$\chi_{1476}(161, \cdot)$$ 1476.2.x.a 28 4
1476.2.x.b 28
1476.2.y $$\chi_{1476}(55, \cdot)$$ n/a 412 4
1476.2.bb $$\chi_{1476}(433, \cdot)$$ 1476.2.bb.a 8 4
1476.2.bb.b 16
1476.2.bb.c 24
1476.2.bb.d 24
1476.2.bd $$\chi_{1476}(107, \cdot)$$ n/a 336 4
1476.2.be $$\chi_{1476}(215, \cdot)$$ n/a 336 4
1476.2.bg $$\chi_{1476}(155, \cdot)$$ n/a 992 4
1476.2.bi $$\chi_{1476}(337, \cdot)$$ n/a 168 4
1476.2.bk $$\chi_{1476}(133, \cdot)$$ n/a 336 8
1476.2.bl $$\chi_{1476}(143, \cdot)$$ n/a 672 8
1476.2.bn $$\chi_{1476}(289, \cdot)$$ n/a 136 8
1476.2.bp $$\chi_{1476}(79, \cdot)$$ n/a 1984 8
1476.2.bq $$\chi_{1476}(137, \cdot)$$ n/a 336 8
1476.2.bu $$\chi_{1476}(59, \cdot)$$ n/a 1984 8
1476.2.bv $$\chi_{1476}(23, \cdot)$$ n/a 1984 8
1476.2.bx $$\chi_{1476}(25, \cdot)$$ n/a 336 8
1476.2.ca $$\chi_{1476}(19, \cdot)$$ n/a 1648 16
1476.2.cb $$\chi_{1476}(17, \cdot)$$ n/a 224 16
1476.2.cf $$\chi_{1476}(49, \cdot)$$ n/a 672 16
1476.2.ch $$\chi_{1476}(131, \cdot)$$ n/a 3968 16
1476.2.ck $$\chi_{1476}(29, \cdot)$$ n/a 1344 32
1476.2.cl $$\chi_{1476}(7, \cdot)$$ n/a 7936 32

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1476))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1476)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(123))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(246))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(369))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(492))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(738))$$$$^{\oplus 2}$$