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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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