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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

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

Display 100 coefficients 10 coefficients

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 available 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

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