# Properties

 Label 2624.2 Level 2624 Weight 2 Dimension 119958 Nonzero newspaces 44 Sturm bound 860160 Trace bound 12

## Defining parameters

 Level: $$N$$ = $$2624 = 2^{6} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$860160$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2624))$$.

Total New Old
Modular forms 217920 121674 96246
Cusp forms 212161 119958 92203
Eisenstein series 5759 1716 4043

## Trace form

 $$119958q - 304q^{2} - 228q^{3} - 304q^{4} - 304q^{5} - 304q^{6} - 224q^{7} - 304q^{8} - 374q^{9} + O(q^{10})$$ $$119958q - 304q^{2} - 228q^{3} - 304q^{4} - 304q^{5} - 304q^{6} - 224q^{7} - 304q^{8} - 374q^{9} - 304q^{10} - 220q^{11} - 304q^{12} - 288q^{13} - 304q^{14} - 216q^{15} - 304q^{16} - 516q^{17} - 304q^{18} - 212q^{19} - 304q^{20} - 312q^{21} - 320q^{22} - 224q^{23} - 384q^{24} - 402q^{25} - 384q^{26} - 240q^{27} - 384q^{28} - 336q^{29} - 464q^{30} - 272q^{31} - 384q^{32} - 280q^{33} - 384q^{34} - 232q^{35} - 464q^{36} - 320q^{37} - 384q^{38} - 224q^{39} - 384q^{40} - 390q^{41} - 704q^{42} - 204q^{43} - 320q^{44} - 296q^{45} - 304q^{46} - 192q^{47} - 304q^{48} - 514q^{49} - 256q^{50} - 280q^{51} - 208q^{52} - 256q^{53} - 176q^{54} - 352q^{55} - 192q^{56} - 368q^{57} - 160q^{58} - 364q^{59} - 112q^{60} - 288q^{61} - 240q^{62} - 360q^{63} - 112q^{64} - 832q^{65} - 144q^{66} - 404q^{67} - 208q^{68} - 280q^{69} - 112q^{70} - 352q^{71} - 160q^{72} - 380q^{73} - 192q^{74} - 340q^{75} - 176q^{76} - 312q^{77} - 256q^{78} - 288q^{79} - 384q^{80} - 538q^{81} - 392q^{82} - 468q^{83} - 528q^{84} - 320q^{85} - 512q^{86} - 224q^{87} - 464q^{88} - 476q^{89} - 592q^{90} - 216q^{91} - 608q^{92} - 384q^{93} - 496q^{94} - 264q^{95} - 576q^{96} - 308q^{97} - 576q^{98} - 276q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2624))$$

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
2624.2.a $$\chi_{2624}(1, \cdot)$$ 2624.2.a.a 1 1
2624.2.a.b 1
2624.2.a.c 1
2624.2.a.d 1
2624.2.a.e 1
2624.2.a.f 1
2624.2.a.g 1
2624.2.a.h 1
2624.2.a.i 2
2624.2.a.j 2
2624.2.a.k 2
2624.2.a.l 2
2624.2.a.m 2
2624.2.a.n 3
2624.2.a.o 3
2624.2.a.p 3
2624.2.a.q 3
2624.2.a.r 3
2624.2.a.s 3
2624.2.a.t 3
2624.2.a.u 3
2624.2.a.v 4
2624.2.a.w 4
2624.2.a.x 4
2624.2.a.y 4
2624.2.a.z 7
2624.2.a.ba 7
2624.2.a.bb 8
2624.2.b $$\chi_{2624}(1313, \cdot)$$ 2624.2.b.a 2 1
2624.2.b.b 2
2624.2.b.c 4
2624.2.b.d 4
2624.2.b.e 12
2624.2.b.f 28
2624.2.b.g 28
2624.2.d $$\chi_{2624}(2049, \cdot)$$ 2624.2.d.a 2 1
2624.2.d.b 2
2624.2.d.c 2
2624.2.d.d 2
2624.2.d.e 2
2624.2.d.f 2
2624.2.d.g 2
2624.2.d.h 2
2624.2.d.i 2
2624.2.d.j 4
2624.2.d.k 4
2624.2.d.l 4
2624.2.d.m 4
2624.2.d.n 6
2624.2.d.o 6
2624.2.d.p 8
2624.2.d.q 8
2624.2.d.r 10
2624.2.d.s 10
2624.2.g $$\chi_{2624}(737, \cdot)$$ 2624.2.g.a 4 1
2624.2.g.b 8
2624.2.g.c 16
2624.2.g.d 56
2624.2.i $$\chi_{2624}(337, \cdot)$$ n/a 164 2
2624.2.l $$\chi_{2624}(2305, \cdot)$$ n/a 164 2
2624.2.n $$\chi_{2624}(657, \cdot)$$ n/a 160 2
2624.2.o $$\chi_{2624}(81, \cdot)$$ n/a 164 2
2624.2.r $$\chi_{2624}(993, \cdot)$$ n/a 168 2
2624.2.t $$\chi_{2624}(401, \cdot)$$ n/a 164 2
2624.2.u $$\chi_{2624}(385, \cdot)$$ n/a 328 4
2624.2.v $$\chi_{2624}(167, \cdot)$$ None 0 4
2624.2.x $$\chi_{2624}(79, \cdot)$$ n/a 328 4
2624.2.ba $$\chi_{2624}(73, \cdot)$$ None 0 4
2624.2.bc $$\chi_{2624}(407, \cdot)$$ None 0 4
2624.2.be $$\chi_{2624}(519, \cdot)$$ None 0 4
2624.2.bf $$\chi_{2624}(329, \cdot)$$ None 0 4
2624.2.bj $$\chi_{2624}(735, \cdot)$$ n/a 336 4
2624.2.bk $$\chi_{2624}(191, \cdot)$$ n/a 328 4
2624.2.bm $$\chi_{2624}(409, \cdot)$$ None 0 4
2624.2.bo $$\chi_{2624}(9, \cdot)$$ None 0 4
2624.2.bp $$\chi_{2624}(495, \cdot)$$ n/a 328 4
2624.2.bs $$\chi_{2624}(55, \cdot)$$ None 0 4
2624.2.bu $$\chi_{2624}(769, \cdot)$$ n/a 328 4
2624.2.bw $$\chi_{2624}(1185, \cdot)$$ n/a 336 4
2624.2.by $$\chi_{2624}(353, \cdot)$$ n/a 336 4
2624.2.ca $$\chi_{2624}(219, \cdot)$$ n/a 2672 8
2624.2.cd $$\chi_{2624}(173, \cdot)$$ n/a 2672 8
2624.2.ce $$\chi_{2624}(245, \cdot)$$ n/a 2672 8
2624.2.cf $$\chi_{2624}(165, \cdot)$$ n/a 2560 8
2624.2.cg $$\chi_{2624}(355, \cdot)$$ n/a 2672 8
2624.2.ch $$\chi_{2624}(331, \cdot)$$ n/a 2672 8
2624.2.cm $$\chi_{2624}(237, \cdot)$$ n/a 2672 8
2624.2.co $$\chi_{2624}(3, \cdot)$$ n/a 2672 8
2624.2.cr $$\chi_{2624}(241, \cdot)$$ n/a 656 8
2624.2.cs $$\chi_{2624}(33, \cdot)$$ n/a 672 8
2624.2.cv $$\chi_{2624}(113, \cdot)$$ n/a 656 8
2624.2.cw $$\chi_{2624}(305, \cdot)$$ n/a 656 8
2624.2.cy $$\chi_{2624}(449, \cdot)$$ n/a 656 8
2624.2.da $$\chi_{2624}(49, \cdot)$$ n/a 656 8
2624.2.dd $$\chi_{2624}(135, \cdot)$$ None 0 16
2624.2.df $$\chi_{2624}(15, \cdot)$$ n/a 1312 16
2624.2.dg $$\chi_{2624}(169, \cdot)$$ None 0 16
2624.2.di $$\chi_{2624}(199, \cdot)$$ None 0 16
2624.2.dk $$\chi_{2624}(151, \cdot)$$ None 0 16
2624.2.dm $$\chi_{2624}(25, \cdot)$$ None 0 16
2624.2.do $$\chi_{2624}(63, \cdot)$$ n/a 1312 16
2624.2.dp $$\chi_{2624}(95, \cdot)$$ n/a 1344 16
2624.2.dt $$\chi_{2624}(57, \cdot)$$ None 0 16
2624.2.du $$\chi_{2624}(121, \cdot)$$ None 0 16
2624.2.dx $$\chi_{2624}(47, \cdot)$$ n/a 1312 16
2624.2.dy $$\chi_{2624}(7, \cdot)$$ None 0 16
2624.2.eb $$\chi_{2624}(259, \cdot)$$ n/a 10688 32
2624.2.ed $$\chi_{2624}(5, \cdot)$$ n/a 10688 32
2624.2.ei $$\chi_{2624}(67, \cdot)$$ n/a 10688 32
2624.2.ej $$\chi_{2624}(11, \cdot)$$ n/a 10688 32
2624.2.ek $$\chi_{2624}(37, \cdot)$$ n/a 10688 32
2624.2.el $$\chi_{2624}(45, \cdot)$$ n/a 10688 32
2624.2.em $$\chi_{2624}(197, \cdot)$$ n/a 10688 32
2624.2.ep $$\chi_{2624}(275, \cdot)$$ n/a 10688 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2624))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2624)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(328))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(656))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1312))$$$$^{\oplus 2}$$