# Properties

 Label 480.2 Level 480 Weight 2 Dimension 2316 Nonzero newspaces 20 Newform subspaces 48 Sturm bound 24576 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$480 = 2^{5} \cdot 3 \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$48$$ Sturm bound: $$24576$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(480))$$.

Total New Old
Modular forms 6656 2436 4220
Cusp forms 5633 2316 3317
Eisenstein series 1023 120 903

## Trace form

 $$2316 q - 8 q^{3} - 16 q^{4} - 4 q^{5} - 24 q^{6} - 16 q^{7} - 20 q^{9} + O(q^{10})$$ $$2316 q - 8 q^{3} - 16 q^{4} - 4 q^{5} - 24 q^{6} - 16 q^{7} - 20 q^{9} - 8 q^{10} + 24 q^{12} + 8 q^{13} + 64 q^{14} + 32 q^{16} + 32 q^{17} + 8 q^{18} + 8 q^{19} + 32 q^{20} + 8 q^{21} + 32 q^{22} + 48 q^{23} - 32 q^{24} - 28 q^{25} - 80 q^{26} + 64 q^{27} - 96 q^{28} + 8 q^{29} - 60 q^{30} + 88 q^{31} - 80 q^{32} + 8 q^{33} - 64 q^{34} + 96 q^{35} - 128 q^{36} + 24 q^{37} - 80 q^{38} + 56 q^{39} - 64 q^{40} + 48 q^{41} - 128 q^{42} + 48 q^{43} - 16 q^{44} - 32 q^{45} - 48 q^{46} - 112 q^{48} - 28 q^{49} - 24 q^{50} - 40 q^{51} - 112 q^{52} + 40 q^{53} - 112 q^{54} - 40 q^{55} - 112 q^{56} - 80 q^{57} - 160 q^{58} - 128 q^{59} - 136 q^{60} + 72 q^{61} - 96 q^{62} - 64 q^{63} - 256 q^{64} - 72 q^{65} - 200 q^{66} - 160 q^{67} - 208 q^{68} + 24 q^{69} - 336 q^{70} - 144 q^{71} - 128 q^{72} - 72 q^{73} - 288 q^{74} - 76 q^{75} - 304 q^{76} - 64 q^{77} - 184 q^{78} - 136 q^{79} - 264 q^{80} - 68 q^{81} - 176 q^{82} - 80 q^{83} - 48 q^{84} - 152 q^{85} - 128 q^{86} - 208 q^{87} - 192 q^{88} - 128 q^{89} - 120 q^{90} - 96 q^{91} - 128 q^{92} - 128 q^{93} - 64 q^{94} - 64 q^{95} + 128 q^{96} - 88 q^{97} + 64 q^{98} - 232 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$

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
480.2.a $$\chi_{480}(1, \cdot)$$ 480.2.a.a 1 1
480.2.a.b 1
480.2.a.c 1
480.2.a.d 1
480.2.a.e 1
480.2.a.f 1
480.2.a.g 1
480.2.a.h 1
480.2.b $$\chi_{480}(431, \cdot)$$ 480.2.b.a 8 1
480.2.b.b 8
480.2.d $$\chi_{480}(49, \cdot)$$ 480.2.d.a 6 1
480.2.d.b 6
480.2.f $$\chi_{480}(289, \cdot)$$ 480.2.f.a 2 1
480.2.f.b 2
480.2.f.c 2
480.2.f.d 2
480.2.f.e 4
480.2.h $$\chi_{480}(191, \cdot)$$ 480.2.h.a 4 1
480.2.h.b 4
480.2.h.c 4
480.2.h.d 4
480.2.k $$\chi_{480}(241, \cdot)$$ 480.2.k.a 2 1
480.2.k.b 6
480.2.m $$\chi_{480}(239, \cdot)$$ 480.2.m.a 4 1
480.2.m.b 16
480.2.o $$\chi_{480}(479, \cdot)$$ 480.2.o.a 24 1
480.2.s $$\chi_{480}(121, \cdot)$$ None 0 2
480.2.t $$\chi_{480}(119, \cdot)$$ None 0 2
480.2.v $$\chi_{480}(257, \cdot)$$ 480.2.v.a 4 2
480.2.v.b 4
480.2.v.c 16
480.2.v.d 24
480.2.w $$\chi_{480}(127, \cdot)$$ 480.2.w.a 4 2
480.2.w.b 4
480.2.w.c 8
480.2.w.d 8
480.2.y $$\chi_{480}(7, \cdot)$$ None 0 2
480.2.bb $$\chi_{480}(233, \cdot)$$ None 0 2
480.2.bc $$\chi_{480}(103, \cdot)$$ None 0 2
480.2.bf $$\chi_{480}(137, \cdot)$$ None 0 2
480.2.bh $$\chi_{480}(367, \cdot)$$ 480.2.bh.a 24 2
480.2.bi $$\chi_{480}(17, \cdot)$$ 480.2.bi.a 4 2
480.2.bi.b 4
480.2.bi.c 32
480.2.bk $$\chi_{480}(71, \cdot)$$ None 0 2
480.2.bl $$\chi_{480}(169, \cdot)$$ None 0 2
480.2.bo $$\chi_{480}(43, \cdot)$$ 480.2.bo.a 192 4
480.2.br $$\chi_{480}(173, \cdot)$$ 480.2.br.a 368 4
480.2.bs $$\chi_{480}(59, \cdot)$$ 480.2.bs.a 16 4
480.2.bs.b 352
480.2.bv $$\chi_{480}(61, \cdot)$$ 480.2.bv.a 56 4
480.2.bv.b 72
480.2.bx $$\chi_{480}(11, \cdot)$$ 480.2.bx.a 256 4
480.2.by $$\chi_{480}(109, \cdot)$$ 480.2.by.a 192 4
480.2.cb $$\chi_{480}(53, \cdot)$$ 480.2.cb.a 368 4
480.2.cc $$\chi_{480}(163, \cdot)$$ 480.2.cc.a 192 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(480))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(480)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$