# Properties

 Label 2520.2 Level 2520 Weight 2 Dimension 64354 Nonzero newspaces 90 Sturm bound 663552 Trace bound 40

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## Defining parameters

 Level: $$N$$ = $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$90$$ Sturm bound: $$663552$$ Trace bound: $$40$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2520))$$.

Total New Old
Modular forms 170496 65434 105062
Cusp forms 161281 64354 96927
Eisenstein series 9215 1080 8135

## Trace form

 $$64354 q - 20 q^{2} - 28 q^{3} - 20 q^{4} + 10 q^{5} - 112 q^{6} - 24 q^{7} - 104 q^{8} - 68 q^{9} + O(q^{10})$$ $$64354 q - 20 q^{2} - 28 q^{3} - 20 q^{4} + 10 q^{5} - 112 q^{6} - 24 q^{7} - 104 q^{8} - 68 q^{9} - 138 q^{10} - 108 q^{11} - 72 q^{12} + 8 q^{13} - 64 q^{14} - 160 q^{15} - 132 q^{16} - 96 q^{17} - 16 q^{18} - 156 q^{19} - 68 q^{20} - 32 q^{21} - 92 q^{22} - 192 q^{23} + 80 q^{24} - 128 q^{25} - 40 q^{26} - 64 q^{27} - 148 q^{28} - 60 q^{29} + 52 q^{30} - 288 q^{31} + 120 q^{32} - 156 q^{33} - 76 q^{34} - 138 q^{35} - 24 q^{36} - 136 q^{37} + 208 q^{38} + 24 q^{39} + 40 q^{40} - 312 q^{41} + 92 q^{42} - 92 q^{43} + 356 q^{44} - 44 q^{45} + 56 q^{46} + 16 q^{47} + 176 q^{48} - 206 q^{49} + 244 q^{50} - 20 q^{51} + 264 q^{52} - 80 q^{53} + 192 q^{54} - 72 q^{55} + 104 q^{56} - 148 q^{57} + 296 q^{58} + 144 q^{59} + 104 q^{60} - 60 q^{61} + 200 q^{62} + 104 q^{63} + 172 q^{64} - 52 q^{65} - 128 q^{66} + 28 q^{67} + 260 q^{68} + 208 q^{69} + 236 q^{70} + 256 q^{71} - 168 q^{73} + 308 q^{74} + 280 q^{75} + 284 q^{76} + 252 q^{77} + 40 q^{78} + 248 q^{79} + 320 q^{80} + 84 q^{81} + 540 q^{82} + 668 q^{83} + 304 q^{84} - 4 q^{85} + 356 q^{86} + 480 q^{87} + 468 q^{88} + 248 q^{89} + 160 q^{90} + 132 q^{91} + 580 q^{92} + 296 q^{93} + 516 q^{94} + 576 q^{95} + 448 q^{96} + 32 q^{97} + 548 q^{98} + 504 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2520))$$

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
2520.2.a $$\chi_{2520}(1, \cdot)$$ 2520.2.a.a 1 1
2520.2.a.b 1
2520.2.a.c 1
2520.2.a.d 1
2520.2.a.e 1
2520.2.a.f 1
2520.2.a.g 1
2520.2.a.h 1
2520.2.a.i 1
2520.2.a.j 1
2520.2.a.k 1
2520.2.a.l 1
2520.2.a.m 1
2520.2.a.n 1
2520.2.a.o 1
2520.2.a.p 1
2520.2.a.q 1
2520.2.a.r 1
2520.2.a.s 1
2520.2.a.t 1
2520.2.a.u 2
2520.2.a.v 2
2520.2.a.w 2
2520.2.a.x 2
2520.2.a.y 2
2520.2.d $$\chi_{2520}(2071, \cdot)$$ None 0 1
2520.2.e $$\chi_{2520}(1331, \cdot)$$ 2520.2.e.a 48 1
2520.2.e.b 48
2520.2.f $$\chi_{2520}(881, \cdot)$$ 2520.2.f.a 8 1
2520.2.f.b 8
2520.2.f.c 8
2520.2.f.d 8
2520.2.g $$\chi_{2520}(1261, \cdot)$$ n/a 120 1
2520.2.j $$\chi_{2520}(2269, \cdot)$$ n/a 180 1
2520.2.k $$\chi_{2520}(1889, \cdot)$$ 2520.2.k.a 24 1
2520.2.k.b 24
2520.2.p $$\chi_{2520}(2339, \cdot)$$ n/a 144 1
2520.2.q $$\chi_{2520}(559, \cdot)$$ None 0 1
2520.2.t $$\chi_{2520}(1009, \cdot)$$ 2520.2.t.a 2 1
2520.2.t.b 2
2520.2.t.c 2
2520.2.t.d 2
2520.2.t.e 2
2520.2.t.f 4
2520.2.t.g 6
2520.2.t.h 6
2520.2.t.i 6
2520.2.t.j 6
2520.2.t.k 6
2520.2.u $$\chi_{2520}(629, \cdot)$$ n/a 192 1
2520.2.v $$\chi_{2520}(1079, \cdot)$$ None 0 1
2520.2.w $$\chi_{2520}(1819, \cdot)$$ n/a 236 1
2520.2.z $$\chi_{2520}(811, \cdot)$$ n/a 160 1
2520.2.ba $$\chi_{2520}(71, \cdot)$$ None 0 1
2520.2.bf $$\chi_{2520}(2141, \cdot)$$ n/a 128 1
2520.2.bg $$\chi_{2520}(121, \cdot)$$ n/a 192 2
2520.2.bh $$\chi_{2520}(841, \cdot)$$ n/a 144 2
2520.2.bi $$\chi_{2520}(361, \cdot)$$ 2520.2.bi.a 2 2
2520.2.bi.b 2
2520.2.bi.c 2
2520.2.bi.d 2
2520.2.bi.e 2
2520.2.bi.f 2
2520.2.bi.g 2
2520.2.bi.h 2
2520.2.bi.i 2
2520.2.bi.j 4
2520.2.bi.k 4
2520.2.bi.l 4
2520.2.bi.m 6
2520.2.bi.n 6
2520.2.bi.o 6
2520.2.bi.p 6
2520.2.bi.q 6
2520.2.bi.r 10
2520.2.bi.s 10
2520.2.bj $$\chi_{2520}(961, \cdot)$$ n/a 192 2
2520.2.bm $$\chi_{2520}(1693, \cdot)$$ n/a 472 2
2520.2.bn $$\chi_{2520}(953, \cdot)$$ 2520.2.bn.a 16 2
2520.2.bn.b 16
2520.2.bn.c 20
2520.2.bn.d 20
2520.2.bo $$\chi_{2520}(127, \cdot)$$ None 0 2
2520.2.bp $$\chi_{2520}(1763, \cdot)$$ n/a 384 2
2520.2.bu $$\chi_{2520}(883, \cdot)$$ n/a 360 2
2520.2.bv $$\chi_{2520}(503, \cdot)$$ None 0 2
2520.2.bw $$\chi_{2520}(433, \cdot)$$ n/a 120 2
2520.2.bx $$\chi_{2520}(197, \cdot)$$ n/a 288 2
2520.2.ca $$\chi_{2520}(1859, \cdot)$$ n/a 1136 2
2520.2.cb $$\chi_{2520}(439, \cdot)$$ None 0 2
2520.2.cg $$\chi_{2520}(709, \cdot)$$ n/a 1136 2
2520.2.ch $$\chi_{2520}(689, \cdot)$$ n/a 288 2
2520.2.ck $$\chi_{2520}(2201, \cdot)$$ n/a 192 2
2520.2.cl $$\chi_{2520}(2221, \cdot)$$ n/a 768 2
2520.2.cm $$\chi_{2520}(31, \cdot)$$ None 0 2
2520.2.cn $$\chi_{2520}(851, \cdot)$$ n/a 768 2
2520.2.cs $$\chi_{2520}(19, \cdot)$$ n/a 472 2
2520.2.ct $$\chi_{2520}(359, \cdot)$$ None 0 2
2520.2.cu $$\chi_{2520}(269, \cdot)$$ n/a 384 2
2520.2.cv $$\chi_{2520}(289, \cdot)$$ n/a 120 2
2520.2.cy $$\chi_{2520}(911, \cdot)$$ None 0 2
2520.2.cz $$\chi_{2520}(1651, \cdot)$$ n/a 768 2
2520.2.dc $$\chi_{2520}(101, \cdot)$$ n/a 768 2
2520.2.dh $$\chi_{2520}(1031, \cdot)$$ None 0 2
2520.2.di $$\chi_{2520}(2131, \cdot)$$ n/a 768 2
2520.2.dl $$\chi_{2520}(461, \cdot)$$ n/a 768 2
2520.2.do $$\chi_{2520}(1469, \cdot)$$ n/a 1136 2
2520.2.dp $$\chi_{2520}(169, \cdot)$$ n/a 216 2
2520.2.ds $$\chi_{2520}(619, \cdot)$$ n/a 1136 2
2520.2.dt $$\chi_{2520}(2039, \cdot)$$ None 0 2
2520.2.du $$\chi_{2520}(509, \cdot)$$ n/a 1136 2
2520.2.dv $$\chi_{2520}(529, \cdot)$$ n/a 288 2
2520.2.dy $$\chi_{2520}(139, \cdot)$$ n/a 1136 2
2520.2.dz $$\chi_{2520}(239, \cdot)$$ None 0 2
2520.2.ec $$\chi_{2520}(341, \cdot)$$ n/a 256 2
2520.2.eh $$\chi_{2520}(431, \cdot)$$ None 0 2
2520.2.ei $$\chi_{2520}(451, \cdot)$$ n/a 320 2
2520.2.el $$\chi_{2520}(541, \cdot)$$ n/a 320 2
2520.2.em $$\chi_{2520}(521, \cdot)$$ 2520.2.em.a 32 2
2520.2.em.b 32
2520.2.en $$\chi_{2520}(611, \cdot)$$ n/a 256 2
2520.2.eo $$\chi_{2520}(271, \cdot)$$ None 0 2
2520.2.er $$\chi_{2520}(209, \cdot)$$ n/a 288 2
2520.2.es $$\chi_{2520}(589, \cdot)$$ n/a 864 2
2520.2.ev $$\chi_{2520}(1879, \cdot)$$ None 0 2
2520.2.ew $$\chi_{2520}(779, \cdot)$$ n/a 1136 2
2520.2.fb $$\chi_{2520}(1769, \cdot)$$ n/a 288 2
2520.2.fc $$\chi_{2520}(1789, \cdot)$$ n/a 1136 2
2520.2.ff $$\chi_{2520}(1399, \cdot)$$ None 0 2
2520.2.fg $$\chi_{2520}(659, \cdot)$$ n/a 864 2
2520.2.fj $$\chi_{2520}(491, \cdot)$$ n/a 576 2
2520.2.fk $$\chi_{2520}(391, \cdot)$$ None 0 2
2520.2.fn $$\chi_{2520}(781, \cdot)$$ n/a 768 2
2520.2.fo $$\chi_{2520}(761, \cdot)$$ n/a 192 2
2520.2.fp $$\chi_{2520}(11, \cdot)$$ n/a 768 2
2520.2.fq $$\chi_{2520}(871, \cdot)$$ None 0 2
2520.2.ft $$\chi_{2520}(421, \cdot)$$ n/a 576 2
2520.2.fu $$\chi_{2520}(41, \cdot)$$ n/a 192 2
2520.2.fx $$\chi_{2520}(199, \cdot)$$ None 0 2
2520.2.fy $$\chi_{2520}(179, \cdot)$$ n/a 384 2
2520.2.gd $$\chi_{2520}(89, \cdot)$$ 2520.2.gd.a 48 2
2520.2.gd.b 48
2520.2.ge $$\chi_{2520}(109, \cdot)$$ n/a 472 2
2520.2.gf $$\chi_{2520}(941, \cdot)$$ n/a 768 2
2520.2.gk $$\chi_{2520}(691, \cdot)$$ n/a 768 2
2520.2.gl $$\chi_{2520}(191, \cdot)$$ None 0 2
2520.2.go $$\chi_{2520}(599, \cdot)$$ None 0 2
2520.2.gp $$\chi_{2520}(1699, \cdot)$$ n/a 1136 2
2520.2.gq $$\chi_{2520}(1969, \cdot)$$ n/a 288 2
2520.2.gr $$\chi_{2520}(1949, \cdot)$$ n/a 1136 2
2520.2.gw $$\chi_{2520}(563, \cdot)$$ n/a 2272 4
2520.2.gx $$\chi_{2520}(583, \cdot)$$ None 0 4
2520.2.gy $$\chi_{2520}(473, \cdot)$$ n/a 576 4
2520.2.gz $$\chi_{2520}(157, \cdot)$$ n/a 2272 4
2520.2.hc $$\chi_{2520}(167, \cdot)$$ None 0 4
2520.2.hd $$\chi_{2520}(43, \cdot)$$ n/a 1728 4
2520.2.hg $$\chi_{2520}(53, \cdot)$$ n/a 768 4
2520.2.hh $$\chi_{2520}(73, \cdot)$$ n/a 240 4
2520.2.hk $$\chi_{2520}(1753, \cdot)$$ n/a 576 4
2520.2.hl $$\chi_{2520}(653, \cdot)$$ n/a 2272 4
2520.2.hq $$\chi_{2520}(403, \cdot)$$ n/a 2272 4
2520.2.hr $$\chi_{2520}(383, \cdot)$$ None 0 4
2520.2.hu $$\chi_{2520}(143, \cdot)$$ None 0 4
2520.2.hv $$\chi_{2520}(163, \cdot)$$ n/a 944 4
2520.2.hy $$\chi_{2520}(533, \cdot)$$ n/a 1728 4
2520.2.hz $$\chi_{2520}(97, \cdot)$$ n/a 576 4
2520.2.ia $$\chi_{2520}(113, \cdot)$$ n/a 432 4
2520.2.ib $$\chi_{2520}(13, \cdot)$$ n/a 2272 4
2520.2.ie $$\chi_{2520}(467, \cdot)$$ n/a 768 4
2520.2.if $$\chi_{2520}(487, \cdot)$$ None 0 4
2520.2.ii $$\chi_{2520}(247, \cdot)$$ None 0 4
2520.2.ij $$\chi_{2520}(227, \cdot)$$ n/a 2272 4
2520.2.io $$\chi_{2520}(493, \cdot)$$ n/a 2272 4
2520.2.ip $$\chi_{2520}(137, \cdot)$$ n/a 576 4
2520.2.is $$\chi_{2520}(233, \cdot)$$ n/a 192 4
2520.2.it $$\chi_{2520}(397, \cdot)$$ n/a 944 4
2520.2.iw $$\chi_{2520}(83, \cdot)$$ n/a 2272 4
2520.2.ix $$\chi_{2520}(463, \cdot)$$ None 0 4
2520.2.ja $$\chi_{2520}(317, \cdot)$$ n/a 2272 4
2520.2.jb $$\chi_{2520}(313, \cdot)$$ n/a 576 4
2520.2.jc $$\chi_{2520}(47, \cdot)$$ None 0 4
2520.2.jd $$\chi_{2520}(67, \cdot)$$ n/a 2272 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2520))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2520)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(630))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(840))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1260))$$$$^{\oplus 2}$$