# Properties

 Label 1520.2 Level 1520 Weight 2 Dimension 34982 Nonzero newspaces 42 Sturm bound 276480 Trace bound 14

## Defining parameters

 Level: $$N$$ = $$1520 = 2^{4} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$276480$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1520))$$.

Total New Old
Modular forms 71136 35902 35234
Cusp forms 67105 34982 32123
Eisenstein series 4031 920 3111

## Trace form

 $$34982 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 119 q^{5} - 168 q^{6} - 42 q^{7} - 40 q^{8} - 10 q^{9} + O(q^{10})$$ $$34982 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 119 q^{5} - 168 q^{6} - 42 q^{7} - 40 q^{8} - 10 q^{9} - 92 q^{10} - 130 q^{11} - 72 q^{12} - 70 q^{13} - 72 q^{14} - 37 q^{15} - 216 q^{16} - 126 q^{17} - 48 q^{18} - 26 q^{19} - 192 q^{20} - 182 q^{21} - 56 q^{22} - 18 q^{23} - 56 q^{24} - 7 q^{25} - 168 q^{26} - 62 q^{27} - 88 q^{28} - 50 q^{29} - 164 q^{30} - 218 q^{31} - 104 q^{32} - 194 q^{33} - 168 q^{34} - 101 q^{35} - 328 q^{36} - 108 q^{37} - 144 q^{38} - 148 q^{39} - 268 q^{40} - 110 q^{41} - 216 q^{42} - 34 q^{43} - 184 q^{44} - 171 q^{45} - 264 q^{46} + 22 q^{47} - 152 q^{48} - 130 q^{49} - 204 q^{50} - 90 q^{51} - 136 q^{52} - 78 q^{53} - 152 q^{54} - 41 q^{55} - 216 q^{56} + 22 q^{57} - 176 q^{58} + 2 q^{59} - 28 q^{60} - 198 q^{61} + 8 q^{62} + 38 q^{63} - 8 q^{64} - 71 q^{65} - 40 q^{66} + 62 q^{67} + 56 q^{68} + 30 q^{69} + 68 q^{70} - 142 q^{71} + 200 q^{72} + 242 q^{73} + 120 q^{74} - 266 q^{75} - 112 q^{76} + 52 q^{77} + 200 q^{78} + 22 q^{79} + 84 q^{80} - 154 q^{81} + 72 q^{82} - 118 q^{83} + 216 q^{84} - 43 q^{85} - 56 q^{86} - 70 q^{87} + 152 q^{88} + 174 q^{89} + 140 q^{90} - 42 q^{91} - 72 q^{92} + 94 q^{93} - 8 q^{94} - 133 q^{95} - 336 q^{96} - 86 q^{97} - 144 q^{98} - 198 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1520))$$

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
1520.2.a $$\chi_{1520}(1, \cdot)$$ 1520.2.a.a 1 1
1520.2.a.b 1
1520.2.a.c 1
1520.2.a.d 1
1520.2.a.e 1
1520.2.a.f 1
1520.2.a.g 1
1520.2.a.h 1
1520.2.a.i 1
1520.2.a.j 1
1520.2.a.k 2
1520.2.a.l 2
1520.2.a.m 2
1520.2.a.n 2
1520.2.a.o 2
1520.2.a.p 3
1520.2.a.q 3
1520.2.a.r 3
1520.2.a.s 3
1520.2.a.t 4
1520.2.d $$\chi_{1520}(609, \cdot)$$ 1520.2.d.a 2 1
1520.2.d.b 2
1520.2.d.c 4
1520.2.d.d 4
1520.2.d.e 4
1520.2.d.f 4
1520.2.d.g 4
1520.2.d.h 6
1520.2.d.i 6
1520.2.d.j 6
1520.2.d.k 12
1520.2.e $$\chi_{1520}(151, \cdot)$$ None 0 1
1520.2.f $$\chi_{1520}(761, \cdot)$$ None 0 1
1520.2.g $$\chi_{1520}(1519, \cdot)$$ 1520.2.g.a 2 1
1520.2.g.b 2
1520.2.g.c 4
1520.2.g.d 4
1520.2.g.e 16
1520.2.g.f 16
1520.2.g.g 16
1520.2.j $$\chi_{1520}(911, \cdot)$$ 1520.2.j.a 2 1
1520.2.j.b 2
1520.2.j.c 8
1520.2.j.d 8
1520.2.j.e 8
1520.2.j.f 12
1520.2.k $$\chi_{1520}(1369, \cdot)$$ None 0 1
1520.2.p $$\chi_{1520}(759, \cdot)$$ None 0 1
1520.2.q $$\chi_{1520}(881, \cdot)$$ 1520.2.q.a 2 2
1520.2.q.b 2
1520.2.q.c 2
1520.2.q.d 2
1520.2.q.e 2
1520.2.q.f 2
1520.2.q.g 2
1520.2.q.h 4
1520.2.q.i 6
1520.2.q.j 6
1520.2.q.k 8
1520.2.q.l 8
1520.2.q.m 8
1520.2.q.n 8
1520.2.q.o 8
1520.2.q.p 10
1520.2.r $$\chi_{1520}(797, \cdot)$$ n/a 472 2
1520.2.t $$\chi_{1520}(1027, \cdot)$$ n/a 432 2
1520.2.w $$\chi_{1520}(379, \cdot)$$ n/a 472 2
1520.2.y $$\chi_{1520}(381, \cdot)$$ n/a 288 2
1520.2.bb $$\chi_{1520}(873, \cdot)$$ None 0 2
1520.2.bc $$\chi_{1520}(1103, \cdot)$$ n/a 108 2
1520.2.bd $$\chi_{1520}(113, \cdot)$$ n/a 116 2
1520.2.be $$\chi_{1520}(343, \cdot)$$ None 0 2
1520.2.bi $$\chi_{1520}(229, \cdot)$$ n/a 432 2
1520.2.bk $$\chi_{1520}(531, \cdot)$$ n/a 320 2
1520.2.bl $$\chi_{1520}(267, \cdot)$$ n/a 432 2
1520.2.bn $$\chi_{1520}(37, \cdot)$$ n/a 472 2
1520.2.bp $$\chi_{1520}(729, \cdot)$$ None 0 2
1520.2.bq $$\chi_{1520}(31, \cdot)$$ 1520.2.bq.a 2 2
1520.2.bq.b 2
1520.2.bq.c 2
1520.2.bq.d 2
1520.2.bq.e 2
1520.2.bq.f 2
1520.2.bq.g 2
1520.2.bq.h 2
1520.2.bq.i 2
1520.2.bq.j 2
1520.2.bq.k 4
1520.2.bq.l 4
1520.2.bq.m 6
1520.2.bq.n 6
1520.2.bq.o 8
1520.2.bq.p 8
1520.2.bq.q 12
1520.2.bq.r 12
1520.2.bv $$\chi_{1520}(1319, \cdot)$$ None 0 2
1520.2.by $$\chi_{1520}(711, \cdot)$$ None 0 2
1520.2.bz $$\chi_{1520}(49, \cdot)$$ n/a 116 2
1520.2.ca $$\chi_{1520}(559, \cdot)$$ n/a 120 2
1520.2.cb $$\chi_{1520}(121, \cdot)$$ None 0 2
1520.2.ce $$\chi_{1520}(81, \cdot)$$ n/a 240 6
1520.2.cf $$\chi_{1520}(597, \cdot)$$ n/a 944 4
1520.2.ch $$\chi_{1520}(83, \cdot)$$ n/a 944 4
1520.2.ck $$\chi_{1520}(501, \cdot)$$ n/a 640 4
1520.2.cm $$\chi_{1520}(179, \cdot)$$ n/a 944 4
1520.2.cn $$\chi_{1520}(217, \cdot)$$ None 0 4
1520.2.co $$\chi_{1520}(463, \cdot)$$ n/a 240 4
1520.2.ct $$\chi_{1520}(673, \cdot)$$ n/a 232 4
1520.2.cu $$\chi_{1520}(7, \cdot)$$ None 0 4
1520.2.cw $$\chi_{1520}(331, \cdot)$$ n/a 640 4
1520.2.cy $$\chi_{1520}(349, \cdot)$$ n/a 944 4
1520.2.cz $$\chi_{1520}(387, \cdot)$$ n/a 944 4
1520.2.db $$\chi_{1520}(293, \cdot)$$ n/a 944 4
1520.2.dd $$\chi_{1520}(279, \cdot)$$ None 0 6
1520.2.di $$\chi_{1520}(441, \cdot)$$ None 0 6
1520.2.dj $$\chi_{1520}(79, \cdot)$$ n/a 360 6
1520.2.dm $$\chi_{1520}(289, \cdot)$$ n/a 348 6
1520.2.dn $$\chi_{1520}(71, \cdot)$$ None 0 6
1520.2.do $$\chi_{1520}(431, \cdot)$$ n/a 240 6
1520.2.dp $$\chi_{1520}(9, \cdot)$$ None 0 6
1520.2.ds $$\chi_{1520}(149, \cdot)$$ n/a 2832 12
1520.2.dt $$\chi_{1520}(51, \cdot)$$ n/a 1920 12
1520.2.dy $$\chi_{1520}(33, \cdot)$$ n/a 696 12
1520.2.dz $$\chi_{1520}(23, \cdot)$$ None 0 12
1520.2.ec $$\chi_{1520}(187, \cdot)$$ n/a 2832 12
1520.2.ed $$\chi_{1520}(13, \cdot)$$ n/a 2832 12
1520.2.eg $$\chi_{1520}(53, \cdot)$$ n/a 2832 12
1520.2.eh $$\chi_{1520}(43, \cdot)$$ n/a 2832 12
1520.2.ek $$\chi_{1520}(393, \cdot)$$ None 0 12
1520.2.el $$\chi_{1520}(47, \cdot)$$ n/a 720 12
1520.2.em $$\chi_{1520}(61, \cdot)$$ n/a 1920 12
1520.2.en $$\chi_{1520}(59, \cdot)$$ n/a 2832 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1520))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1520)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1520))$$$$^{\oplus 1}$$