# Properties

 Label 1480.2 Level 1480 Weight 2 Dimension 33388 Nonzero newspaces 48 Sturm bound 262656 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$1480 = 2^{3} \cdot 5 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$262656$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1480))$$.

Total New Old
Modular forms 67392 34228 33164
Cusp forms 63937 33388 30549
Eisenstein series 3455 840 2615

## Trace form

 $$33388 q - 64 q^{2} - 64 q^{3} - 64 q^{4} + 2 q^{5} - 200 q^{6} - 56 q^{7} - 64 q^{8} - 118 q^{9} + O(q^{10})$$ $$33388 q - 64 q^{2} - 64 q^{3} - 64 q^{4} + 2 q^{5} - 200 q^{6} - 56 q^{7} - 64 q^{8} - 118 q^{9} - 100 q^{10} - 192 q^{11} - 88 q^{12} + 4 q^{13} - 88 q^{14} - 116 q^{15} - 232 q^{16} - 132 q^{17} - 120 q^{18} - 96 q^{19} - 140 q^{20} - 16 q^{21} - 104 q^{22} - 72 q^{23} - 120 q^{24} - 190 q^{25} - 232 q^{26} - 88 q^{27} - 56 q^{28} + 12 q^{29} - 108 q^{30} - 216 q^{31} - 24 q^{32} - 128 q^{33} - 124 q^{35} - 136 q^{36} - 6 q^{37} - 96 q^{38} - 88 q^{39} - 20 q^{40} - 396 q^{41} - 24 q^{42} - 112 q^{43} - 40 q^{44} + 2 q^{45} - 152 q^{46} - 120 q^{47} - 56 q^{48} - 158 q^{49} - 140 q^{50} - 232 q^{51} - 112 q^{52} - 12 q^{53} - 120 q^{54} - 164 q^{55} - 312 q^{56} - 176 q^{57} - 160 q^{58} - 40 q^{59} - 188 q^{60} + 134 q^{61} - 184 q^{62} + 160 q^{63} - 136 q^{64} - 163 q^{65} - 248 q^{66} + 40 q^{67} - 112 q^{68} + 272 q^{69} - 108 q^{70} - 24 q^{71} - 48 q^{72} - 52 q^{73} - 52 q^{74} + 116 q^{75} - 216 q^{76} + 176 q^{77} + 56 q^{78} + 232 q^{79} - 60 q^{80} - 150 q^{81} + 120 q^{83} - 8 q^{84} + 77 q^{85} - 232 q^{86} + 240 q^{87} - 72 q^{88} - 82 q^{89} - 100 q^{90} - 112 q^{91} - 40 q^{92} - 136 q^{94} - 84 q^{95} - 312 q^{96} - 116 q^{97} - 96 q^{98} - 64 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1480))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1480.2.a $$\chi_{1480}(1, \cdot)$$ 1480.2.a.a 1 1
1480.2.a.b 1
1480.2.a.c 1
1480.2.a.d 1
1480.2.a.e 3
1480.2.a.f 3
1480.2.a.g 5
1480.2.a.h 5
1480.2.a.i 5
1480.2.a.j 5
1480.2.a.k 6
1480.2.d $$\chi_{1480}(889, \cdot)$$ 1480.2.d.a 2 1
1480.2.d.b 20
1480.2.d.c 32
1480.2.e $$\chi_{1480}(369, \cdot)$$ 1480.2.e.a 4 1
1480.2.e.b 4
1480.2.e.c 24
1480.2.e.d 24
1480.2.f $$\chi_{1480}(741, \cdot)$$ n/a 144 1
1480.2.g $$\chi_{1480}(221, \cdot)$$ n/a 152 1
1480.2.j $$\chi_{1480}(1109, \cdot)$$ n/a 224 1
1480.2.k $$\chi_{1480}(149, \cdot)$$ n/a 216 1
1480.2.p $$\chi_{1480}(961, \cdot)$$ 1480.2.p.a 2 1
1480.2.p.b 4
1480.2.p.c 12
1480.2.p.d 20
1480.2.q $$\chi_{1480}(121, \cdot)$$ 1480.2.q.a 18 2
1480.2.q.b 18
1480.2.q.c 20
1480.2.q.d 20
1480.2.r $$\chi_{1480}(771, \cdot)$$ n/a 304 2
1480.2.u $$\chi_{1480}(919, \cdot)$$ None 0 2
1480.2.w $$\chi_{1480}(697, \cdot)$$ n/a 114 2
1480.2.y $$\chi_{1480}(887, \cdot)$$ None 0 2
1480.2.ba $$\chi_{1480}(223, \cdot)$$ None 0 2
1480.2.bb $$\chi_{1480}(857, \cdot)$$ n/a 114 2
1480.2.bd $$\chi_{1480}(117, \cdot)$$ n/a 448 2
1480.2.bf $$\chi_{1480}(667, \cdot)$$ n/a 432 2
1480.2.bh $$\chi_{1480}(147, \cdot)$$ n/a 448 2
1480.2.bk $$\chi_{1480}(413, \cdot)$$ n/a 448 2
1480.2.bm $$\chi_{1480}(31, \cdot)$$ None 0 2
1480.2.bn $$\chi_{1480}(179, \cdot)$$ n/a 448 2
1480.2.br $$\chi_{1480}(841, \cdot)$$ 1480.2.br.a 36 2
1480.2.br.b 40
1480.2.bs $$\chi_{1480}(269, \cdot)$$ n/a 448 2
1480.2.bt $$\chi_{1480}(989, \cdot)$$ n/a 448 2
1480.2.bw $$\chi_{1480}(101, \cdot)$$ n/a 304 2
1480.2.bx $$\chi_{1480}(581, \cdot)$$ n/a 304 2
1480.2.cc $$\chi_{1480}(249, \cdot)$$ n/a 112 2
1480.2.cd $$\chi_{1480}(729, \cdot)$$ n/a 116 2
1480.2.ce $$\chi_{1480}(81, \cdot)$$ n/a 228 6
1480.2.cf $$\chi_{1480}(859, \cdot)$$ n/a 896 4
1480.2.ci $$\chi_{1480}(711, \cdot)$$ None 0 4
1480.2.ck $$\chi_{1480}(97, \cdot)$$ n/a 228 4
1480.2.cl $$\chi_{1480}(47, \cdot)$$ None 0 4
1480.2.cn $$\chi_{1480}(767, \cdot)$$ None 0 4
1480.2.cp $$\chi_{1480}(177, \cdot)$$ n/a 228 4
1480.2.cr $$\chi_{1480}(717, \cdot)$$ n/a 896 4
1480.2.cu $$\chi_{1480}(27, \cdot)$$ n/a 896 4
1480.2.cw $$\chi_{1480}(507, \cdot)$$ n/a 896 4
1480.2.cy $$\chi_{1480}(637, \cdot)$$ n/a 896 4
1480.2.da $$\chi_{1480}(119, \cdot)$$ None 0 4
1480.2.db $$\chi_{1480}(51, \cdot)$$ n/a 608 4
1480.2.df $$\chi_{1480}(169, \cdot)$$ n/a 336 6
1480.2.dg $$\chi_{1480}(41, \cdot)$$ n/a 228 6
1480.2.di $$\chi_{1480}(9, \cdot)$$ n/a 348 6
1480.2.dk $$\chi_{1480}(189, \cdot)$$ n/a 1344 6
1480.2.dm $$\chi_{1480}(181, \cdot)$$ n/a 912 6
1480.2.dp $$\chi_{1480}(229, \cdot)$$ n/a 1344 6
1480.2.dr $$\chi_{1480}(21, \cdot)$$ n/a 912 6
1480.2.ds $$\chi_{1480}(533, \cdot)$$ n/a 2688 12
1480.2.dv $$\chi_{1480}(311, \cdot)$$ None 0 12
1480.2.dw $$\chi_{1480}(83, \cdot)$$ n/a 2688 12
1480.2.dz $$\chi_{1480}(3, \cdot)$$ n/a 2688 12
1480.2.ea $$\chi_{1480}(39, \cdot)$$ None 0 12
1480.2.ed $$\chi_{1480}(13, \cdot)$$ n/a 2688 12
1480.2.ef $$\chi_{1480}(17, \cdot)$$ n/a 684 12
1480.2.eg $$\chi_{1480}(19, \cdot)$$ n/a 2688 12
1480.2.ei $$\chi_{1480}(247, \cdot)$$ None 0 12
1480.2.el $$\chi_{1480}(7, \cdot)$$ None 0 12
1480.2.en $$\chi_{1480}(91, \cdot)$$ n/a 1824 12
1480.2.eo $$\chi_{1480}(57, \cdot)$$ n/a 684 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1480))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1480)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(740))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1480))$$$$^{\oplus 1}$$