# Properties

 Label 624.2 Level 624 Weight 2 Dimension 4382 Nonzero newspaces 28 Newform subspaces 120 Sturm bound 43008 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$624 = 2^{4} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Newform subspaces: $$120$$ Sturm bound: $$43008$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(624))$$.

Total New Old
Modular forms 11424 4582 6842
Cusp forms 10081 4382 5699
Eisenstein series 1343 200 1143

## Trace form

 $$4382 q - 16 q^{3} - 32 q^{4} + 4 q^{5} - 8 q^{6} - 20 q^{7} + 24 q^{8} + 4 q^{9} + O(q^{10})$$ $$4382 q - 16 q^{3} - 32 q^{4} + 4 q^{5} - 8 q^{6} - 20 q^{7} + 24 q^{8} + 4 q^{9} - 32 q^{10} + 24 q^{11} - 24 q^{12} - 50 q^{13} - 24 q^{14} + 2 q^{15} - 80 q^{16} - 4 q^{17} - 40 q^{18} - 4 q^{19} - 32 q^{20} - 38 q^{21} - 80 q^{22} - 16 q^{23} - 80 q^{24} - 18 q^{25} - 20 q^{26} - 58 q^{27} - 48 q^{28} + 20 q^{29} - 64 q^{30} - 68 q^{31} - 38 q^{33} - 32 q^{34} - 48 q^{35} - 56 q^{36} + 8 q^{37} + 16 q^{38} - 24 q^{39} - 48 q^{40} + 60 q^{41} + 64 q^{42} + 60 q^{43} + 80 q^{44} + 22 q^{45} + 48 q^{46} + 72 q^{47} + 104 q^{48} + 78 q^{49} + 72 q^{50} - 20 q^{51} - 16 q^{52} + 68 q^{53} + 72 q^{54} + 44 q^{55} + 58 q^{57} - 80 q^{58} + 16 q^{59} - 40 q^{60} - 48 q^{61} + 24 q^{62} - 22 q^{63} - 176 q^{64} + 60 q^{65} - 152 q^{66} - 44 q^{67} - 64 q^{68} - 86 q^{69} - 192 q^{70} + 16 q^{71} - 96 q^{72} - 72 q^{73} - 104 q^{74} + 2 q^{75} - 176 q^{76} - 32 q^{77} - 72 q^{78} - 40 q^{79} - 16 q^{80} - 68 q^{81} - 96 q^{82} + 72 q^{83} - 176 q^{84} - 132 q^{85} - 160 q^{86} + 54 q^{87} - 224 q^{88} - 180 q^{89} - 288 q^{90} - 68 q^{91} - 256 q^{92} - 190 q^{93} - 352 q^{94} - 8 q^{95} - 344 q^{96} - 232 q^{97} - 352 q^{98} + 14 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$

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
624.2.a $$\chi_{624}(1, \cdot)$$ 624.2.a.a 1 1
624.2.a.b 1
624.2.a.c 1
624.2.a.d 1
624.2.a.e 1
624.2.a.f 1
624.2.a.g 1
624.2.a.h 1
624.2.a.i 1
624.2.a.j 1
624.2.a.k 2
624.2.c $$\chi_{624}(337, \cdot)$$ 624.2.c.a 2 1
624.2.c.b 2
624.2.c.c 2
624.2.c.d 2
624.2.c.e 2
624.2.c.f 2
624.2.c.g 2
624.2.d $$\chi_{624}(287, \cdot)$$ 624.2.d.a 2 1
624.2.d.b 2
624.2.d.c 2
624.2.d.d 2
624.2.d.e 2
624.2.d.f 2
624.2.d.g 4
624.2.d.h 4
624.2.d.i 4
624.2.g $$\chi_{624}(313, \cdot)$$ None 0 1
624.2.h $$\chi_{624}(311, \cdot)$$ None 0 1
624.2.j $$\chi_{624}(599, \cdot)$$ None 0 1
624.2.m $$\chi_{624}(25, \cdot)$$ None 0 1
624.2.n $$\chi_{624}(623, \cdot)$$ 624.2.n.a 2 1
624.2.n.b 2
624.2.n.c 4
624.2.n.d 4
624.2.n.e 8
624.2.n.f 8
624.2.q $$\chi_{624}(289, \cdot)$$ 624.2.q.a 2 2
624.2.q.b 2
624.2.q.c 2
624.2.q.d 2
624.2.q.e 2
624.2.q.f 2
624.2.q.g 2
624.2.q.h 4
624.2.q.i 4
624.2.q.j 6
624.2.r $$\chi_{624}(499, \cdot)$$ 624.2.r.a 112 2
624.2.u $$\chi_{624}(5, \cdot)$$ 624.2.u.a 4 2
624.2.u.b 4
624.2.u.c 208
624.2.v $$\chi_{624}(155, \cdot)$$ 624.2.v.a 16 2
624.2.v.b 200
624.2.x $$\chi_{624}(157, \cdot)$$ 624.2.x.a 40 2
624.2.x.b 56
624.2.bb $$\chi_{624}(151, \cdot)$$ None 0 2
624.2.bc $$\chi_{624}(31, \cdot)$$ 624.2.bc.a 2 2
624.2.bc.b 2
624.2.bc.c 4
624.2.bc.d 4
624.2.bc.e 8
624.2.bc.f 8
624.2.bf $$\chi_{624}(161, \cdot)$$ 624.2.bf.a 4 2
624.2.bf.b 4
624.2.bf.c 4
624.2.bf.d 4
624.2.bf.e 8
624.2.bf.f 12
624.2.bf.g 16
624.2.bg $$\chi_{624}(281, \cdot)$$ None 0 2
624.2.bh $$\chi_{624}(131, \cdot)$$ 624.2.bh.a 192 2
624.2.bj $$\chi_{624}(181, \cdot)$$ 624.2.bj.a 112 2
624.2.bm $$\chi_{624}(317, \cdot)$$ 624.2.bm.a 4 2
624.2.bm.b 4
624.2.bm.c 208
624.2.bn $$\chi_{624}(187, \cdot)$$ 624.2.bn.a 112 2
624.2.bq $$\chi_{624}(23, \cdot)$$ None 0 2
624.2.br $$\chi_{624}(217, \cdot)$$ None 0 2
624.2.bu $$\chi_{624}(191, \cdot)$$ 624.2.bu.a 2 2
624.2.bu.b 2
624.2.bu.c 2
624.2.bu.d 2
624.2.bu.e 2
624.2.bu.f 2
624.2.bu.g 2
624.2.bu.h 2
624.2.bu.i 4
624.2.bu.j 4
624.2.bu.k 6
624.2.bu.l 6
624.2.bu.m 6
624.2.bu.n 6
624.2.bu.o 8
624.2.bv $$\chi_{624}(49, \cdot)$$ 624.2.bv.a 2 2
624.2.bv.b 2
624.2.bv.c 4
624.2.bv.d 4
624.2.bv.e 4
624.2.bv.f 4
624.2.bv.g 8
624.2.bz $$\chi_{624}(95, \cdot)$$ 624.2.bz.a 2 2
624.2.bz.b 2
624.2.bz.c 2
624.2.bz.d 2
624.2.bz.e 8
624.2.bz.f 8
624.2.bz.g 16
624.2.bz.h 16
624.2.ca $$\chi_{624}(121, \cdot)$$ None 0 2
624.2.cd $$\chi_{624}(263, \cdot)$$ None 0 2
624.2.ce $$\chi_{624}(149, \cdot)$$ 624.2.ce.a 432 4
624.2.ch $$\chi_{624}(19, \cdot)$$ 624.2.ch.a 224 4
624.2.cj $$\chi_{624}(205, \cdot)$$ 624.2.cj.a 224 4
624.2.cl $$\chi_{624}(35, \cdot)$$ 624.2.cl.a 432 4
624.2.cm $$\chi_{624}(41, \cdot)$$ None 0 4
624.2.cn $$\chi_{624}(305, \cdot)$$ 624.2.cn.a 4 4
624.2.cn.b 4
624.2.cn.c 8
624.2.cn.d 16
624.2.cn.e 16
624.2.cn.f 56
624.2.cq $$\chi_{624}(175, \cdot)$$ 624.2.cq.a 8 4
624.2.cq.b 8
624.2.cq.c 8
624.2.cq.d 8
624.2.cq.e 12
624.2.cq.f 12
624.2.cr $$\chi_{624}(7, \cdot)$$ None 0 4
624.2.cv $$\chi_{624}(61, \cdot)$$ 624.2.cv.a 224 4
624.2.cx $$\chi_{624}(179, \cdot)$$ 624.2.cx.a 432 4
624.2.cz $$\chi_{624}(115, \cdot)$$ 624.2.cz.a 224 4
624.2.da $$\chi_{624}(245, \cdot)$$ 624.2.da.a 432 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(624))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(624)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$