# Properties

 Label 2480.2 Level 2480 Weight 2 Dimension 94058 Nonzero newspaces 56 Sturm bound 737280 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2480 = 2^{4} \cdot 5 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$737280$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2480))$$.

Total New Old
Modular forms 187680 95626 92054
Cusp forms 180961 94058 86903
Eisenstein series 6719 1568 5151

## Trace form

 $$94058 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 209 q^{5} - 312 q^{6} - 78 q^{7} - 88 q^{8} - 22 q^{9} + O(q^{10})$$ $$94058 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 209 q^{5} - 312 q^{6} - 78 q^{7} - 88 q^{8} - 22 q^{9} - 164 q^{10} - 238 q^{11} - 120 q^{12} - 130 q^{13} - 120 q^{14} - 91 q^{15} - 360 q^{16} - 234 q^{17} - 96 q^{18} - 34 q^{19} - 156 q^{20} - 362 q^{21} - 104 q^{22} - 54 q^{23} - 104 q^{24} - 25 q^{25} - 312 q^{26} - 98 q^{27} - 136 q^{28} - 110 q^{29} - 236 q^{30} - 298 q^{31} - 272 q^{32} - 302 q^{33} - 216 q^{34} - 155 q^{35} - 472 q^{36} - 186 q^{37} - 264 q^{38} - 130 q^{39} - 340 q^{40} - 146 q^{41} - 264 q^{42} - 70 q^{43} - 232 q^{44} - 261 q^{45} - 408 q^{46} - 14 q^{47} - 200 q^{48} - 238 q^{49} - 276 q^{50} - 198 q^{51} - 184 q^{52} - 138 q^{53} - 200 q^{54} - 95 q^{55} - 360 q^{56} + 50 q^{57} - 152 q^{58} - 34 q^{59} - 100 q^{60} - 420 q^{61} - 80 q^{62} - 232 q^{63} - 56 q^{64} - 305 q^{65} - 184 q^{66} - 190 q^{67} + 8 q^{68} - 174 q^{69} - 4 q^{70} - 358 q^{71} + 152 q^{72} + 14 q^{73} + 72 q^{74} - 347 q^{75} - 152 q^{76} - 134 q^{77} + 152 q^{78} - 266 q^{79} + 12 q^{80} - 694 q^{81} + 24 q^{82} - 262 q^{83} + 168 q^{84} - 205 q^{85} - 200 q^{86} - 322 q^{87} + 104 q^{88} + 18 q^{89} + 68 q^{90} - 294 q^{91} - 120 q^{92} - 94 q^{93} - 176 q^{94} - 239 q^{95} - 264 q^{96} - 194 q^{97} - 192 q^{98} - 234 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2480))$$

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
2480.2.a $$\chi_{2480}(1, \cdot)$$ 2480.2.a.a 1 1
2480.2.a.b 1
2480.2.a.c 1
2480.2.a.d 1
2480.2.a.e 1
2480.2.a.f 1
2480.2.a.g 1
2480.2.a.h 1
2480.2.a.i 1
2480.2.a.j 1
2480.2.a.k 1
2480.2.a.l 1
2480.2.a.m 1
2480.2.a.n 1
2480.2.a.o 1
2480.2.a.p 2
2480.2.a.q 2
2480.2.a.r 2
2480.2.a.s 2
2480.2.a.t 3
2480.2.a.u 3
2480.2.a.v 3
2480.2.a.w 4
2480.2.a.x 4
2480.2.a.y 4
2480.2.a.z 4
2480.2.a.ba 6
2480.2.a.bb 6
2480.2.b $$\chi_{2480}(2231, \cdot)$$ None 0 1
2480.2.d $$\chi_{2480}(1489, \cdot)$$ 2480.2.d.a 2 1
2480.2.d.b 4
2480.2.d.c 6
2480.2.d.d 8
2480.2.d.e 8
2480.2.d.f 8
2480.2.d.g 10
2480.2.d.h 22
2480.2.d.i 22
2480.2.g $$\chi_{2480}(1241, \cdot)$$ None 0 1
2480.2.i $$\chi_{2480}(2479, \cdot)$$ 2480.2.i.a 8 1
2480.2.i.b 8
2480.2.i.c 16
2480.2.i.d 16
2480.2.i.e 24
2480.2.i.f 24
2480.2.j $$\chi_{2480}(249, \cdot)$$ None 0 1
2480.2.l $$\chi_{2480}(991, \cdot)$$ 2480.2.l.a 2 1
2480.2.l.b 2
2480.2.l.c 12
2480.2.l.d 12
2480.2.l.e 16
2480.2.l.f 20
2480.2.o $$\chi_{2480}(1239, \cdot)$$ None 0 1
2480.2.q $$\chi_{2480}(1121, \cdot)$$ n/a 128 2
2480.2.r $$\chi_{2480}(557, \cdot)$$ n/a 760 2
2480.2.u $$\chi_{2480}(683, \cdot)$$ n/a 720 2
2480.2.x $$\chi_{2480}(621, \cdot)$$ n/a 480 2
2480.2.y $$\chi_{2480}(619, \cdot)$$ n/a 760 2
2480.2.z $$\chi_{2480}(433, \cdot)$$ n/a 188 2
2480.2.bc $$\chi_{2480}(63, \cdot)$$ n/a 180 2
2480.2.bd $$\chi_{2480}(807, \cdot)$$ None 0 2
2480.2.bg $$\chi_{2480}(1177, \cdot)$$ None 0 2
2480.2.bh $$\chi_{2480}(371, \cdot)$$ n/a 512 2
2480.2.bi $$\chi_{2480}(869, \cdot)$$ n/a 720 2
2480.2.bl $$\chi_{2480}(187, \cdot)$$ n/a 720 2
2480.2.bo $$\chi_{2480}(1053, \cdot)$$ n/a 760 2
2480.2.bp $$\chi_{2480}(481, \cdot)$$ n/a 256 4
2480.2.br $$\chi_{2480}(119, \cdot)$$ None 0 2
2480.2.bu $$\chi_{2480}(1711, \cdot)$$ n/a 128 2
2480.2.bw $$\chi_{2480}(1369, \cdot)$$ None 0 2
2480.2.bx $$\chi_{2480}(719, \cdot)$$ n/a 192 2
2480.2.bz $$\chi_{2480}(521, \cdot)$$ None 0 2
2480.2.cc $$\chi_{2480}(129, \cdot)$$ n/a 188 2
2480.2.ce $$\chi_{2480}(471, \cdot)$$ None 0 2
2480.2.cg $$\chi_{2480}(519, \cdot)$$ None 0 4
2480.2.cj $$\chi_{2480}(271, \cdot)$$ n/a 256 4
2480.2.cl $$\chi_{2480}(729, \cdot)$$ None 0 4
2480.2.cm $$\chi_{2480}(399, \cdot)$$ n/a 384 4
2480.2.co $$\chi_{2480}(281, \cdot)$$ None 0 4
2480.2.cr $$\chi_{2480}(529, \cdot)$$ n/a 376 4
2480.2.ct $$\chi_{2480}(151, \cdot)$$ None 0 4
2480.2.cu $$\chi_{2480}(37, \cdot)$$ n/a 1520 4
2480.2.cx $$\chi_{2480}(563, \cdot)$$ n/a 1520 4
2480.2.da $$\chi_{2480}(491, \cdot)$$ n/a 1024 4
2480.2.db $$\chi_{2480}(149, \cdot)$$ n/a 1520 4
2480.2.dc $$\chi_{2480}(57, \cdot)$$ None 0 4
2480.2.df $$\chi_{2480}(87, \cdot)$$ None 0 4
2480.2.dg $$\chi_{2480}(687, \cdot)$$ n/a 384 4
2480.2.dj $$\chi_{2480}(657, \cdot)$$ n/a 376 4
2480.2.dk $$\chi_{2480}(501, \cdot)$$ n/a 1024 4
2480.2.dl $$\chi_{2480}(99, \cdot)$$ n/a 1520 4
2480.2.do $$\chi_{2480}(67, \cdot)$$ n/a 1520 4
2480.2.dr $$\chi_{2480}(533, \cdot)$$ n/a 1520 4
2480.2.ds $$\chi_{2480}(81, \cdot)$$ n/a 512 8
2480.2.du $$\chi_{2480}(277, \cdot)$$ n/a 3040 8
2480.2.dv $$\chi_{2480}(163, \cdot)$$ n/a 3040 8
2480.2.dz $$\chi_{2480}(109, \cdot)$$ n/a 3040 8
2480.2.ea $$\chi_{2480}(91, \cdot)$$ n/a 2048 8
2480.2.eb $$\chi_{2480}(153, \cdot)$$ None 0 8
2480.2.ee $$\chi_{2480}(343, \cdot)$$ None 0 8
2480.2.ef $$\chi_{2480}(47, \cdot)$$ n/a 768 8
2480.2.ei $$\chi_{2480}(337, \cdot)$$ n/a 752 8
2480.2.ej $$\chi_{2480}(139, \cdot)$$ n/a 3040 8
2480.2.ek $$\chi_{2480}(101, \cdot)$$ n/a 2048 8
2480.2.eo $$\chi_{2480}(283, \cdot)$$ n/a 3040 8
2480.2.ep $$\chi_{2480}(77, \cdot)$$ n/a 3040 8
2480.2.er $$\chi_{2480}(551, \cdot)$$ None 0 8
2480.2.et $$\chi_{2480}(49, \cdot)$$ n/a 752 8
2480.2.ew $$\chi_{2480}(41, \cdot)$$ None 0 8
2480.2.ey $$\chi_{2480}(79, \cdot)$$ n/a 768 8
2480.2.ez $$\chi_{2480}(9, \cdot)$$ None 0 8
2480.2.fb $$\chi_{2480}(911, \cdot)$$ n/a 512 8
2480.2.fe $$\chi_{2480}(199, \cdot)$$ None 0 8
2480.2.fh $$\chi_{2480}(53, \cdot)$$ n/a 6080 16
2480.2.fi $$\chi_{2480}(227, \cdot)$$ n/a 6080 16
2480.2.fm $$\chi_{2480}(179, \cdot)$$ n/a 6080 16
2480.2.fn $$\chi_{2480}(381, \cdot)$$ n/a 4096 16
2480.2.fo $$\chi_{2480}(17, \cdot)$$ n/a 1504 16
2480.2.fr $$\chi_{2480}(143, \cdot)$$ n/a 1536 16
2480.2.fs $$\chi_{2480}(7, \cdot)$$ None 0 16
2480.2.fv $$\chi_{2480}(73, \cdot)$$ None 0 16
2480.2.fw $$\chi_{2480}(69, \cdot)$$ n/a 6080 16
2480.2.fx $$\chi_{2480}(11, \cdot)$$ n/a 4096 16
2480.2.gb $$\chi_{2480}(107, \cdot)$$ n/a 6080 16
2480.2.gc $$\chi_{2480}(13, \cdot)$$ n/a 6080 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2480))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2480)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(124))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(248))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(496))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(620))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2480))$$$$^{\oplus 1}$$