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Properties

Label 2624.2
Level 2624
Weight 2
Dimension 119958
Nonzero newspaces 44
Sturm bound 860160
Trace bound 12

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Defining parameters

Level: \( N \) = \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 44 \)
Sturm bound: \(860160\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2624))\).

Total New Old
Modular forms 217920 121674 96246
Cusp forms 212161 119958 92203
Eisenstein series 5759 1716 4043

Trace form

\( 119958 q - 304 q^{2} - 228 q^{3} - 304 q^{4} - 304 q^{5} - 304 q^{6} - 224 q^{7} - 304 q^{8} - 374 q^{9} + O(q^{10}) \) \( 119958 q - 304 q^{2} - 228 q^{3} - 304 q^{4} - 304 q^{5} - 304 q^{6} - 224 q^{7} - 304 q^{8} - 374 q^{9} - 304 q^{10} - 220 q^{11} - 304 q^{12} - 288 q^{13} - 304 q^{14} - 216 q^{15} - 304 q^{16} - 516 q^{17} - 304 q^{18} - 212 q^{19} - 304 q^{20} - 312 q^{21} - 320 q^{22} - 224 q^{23} - 384 q^{24} - 402 q^{25} - 384 q^{26} - 240 q^{27} - 384 q^{28} - 336 q^{29} - 464 q^{30} - 272 q^{31} - 384 q^{32} - 280 q^{33} - 384 q^{34} - 232 q^{35} - 464 q^{36} - 320 q^{37} - 384 q^{38} - 224 q^{39} - 384 q^{40} - 390 q^{41} - 704 q^{42} - 204 q^{43} - 320 q^{44} - 296 q^{45} - 304 q^{46} - 192 q^{47} - 304 q^{48} - 514 q^{49} - 256 q^{50} - 280 q^{51} - 208 q^{52} - 256 q^{53} - 176 q^{54} - 352 q^{55} - 192 q^{56} - 368 q^{57} - 160 q^{58} - 364 q^{59} - 112 q^{60} - 288 q^{61} - 240 q^{62} - 360 q^{63} - 112 q^{64} - 832 q^{65} - 144 q^{66} - 404 q^{67} - 208 q^{68} - 280 q^{69} - 112 q^{70} - 352 q^{71} - 160 q^{72} - 380 q^{73} - 192 q^{74} - 340 q^{75} - 176 q^{76} - 312 q^{77} - 256 q^{78} - 288 q^{79} - 384 q^{80} - 538 q^{81} - 392 q^{82} - 468 q^{83} - 528 q^{84} - 320 q^{85} - 512 q^{86} - 224 q^{87} - 464 q^{88} - 476 q^{89} - 592 q^{90} - 216 q^{91} - 608 q^{92} - 384 q^{93} - 496 q^{94} - 264 q^{95} - 576 q^{96} - 308 q^{97} - 576 q^{98} - 276 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2624))\)

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
2624.2.a \(\chi_{2624}(1, \cdot)\) 2624.2.a.a 1 1
2624.2.a.b 1
2624.2.a.c 1
2624.2.a.d 1
2624.2.a.e 1
2624.2.a.f 1
2624.2.a.g 1
2624.2.a.h 1
2624.2.a.i 2
2624.2.a.j 2
2624.2.a.k 2
2624.2.a.l 2
2624.2.a.m 2
2624.2.a.n 3
2624.2.a.o 3
2624.2.a.p 3
2624.2.a.q 3
2624.2.a.r 3
2624.2.a.s 3
2624.2.a.t 3
2624.2.a.u 3
2624.2.a.v 4
2624.2.a.w 4
2624.2.a.x 4
2624.2.a.y 4
2624.2.a.z 7
2624.2.a.ba 7
2624.2.a.bb 8
2624.2.b \(\chi_{2624}(1313, \cdot)\) 2624.2.b.a 2 1
2624.2.b.b 2
2624.2.b.c 4
2624.2.b.d 4
2624.2.b.e 12
2624.2.b.f 28
2624.2.b.g 28
2624.2.d \(\chi_{2624}(2049, \cdot)\) 2624.2.d.a 2 1
2624.2.d.b 2
2624.2.d.c 2
2624.2.d.d 2
2624.2.d.e 2
2624.2.d.f 2
2624.2.d.g 2
2624.2.d.h 2
2624.2.d.i 2
2624.2.d.j 4
2624.2.d.k 4
2624.2.d.l 4
2624.2.d.m 4
2624.2.d.n 6
2624.2.d.o 6
2624.2.d.p 8
2624.2.d.q 8
2624.2.d.r 10
2624.2.d.s 10
2624.2.g \(\chi_{2624}(737, \cdot)\) 2624.2.g.a 4 1
2624.2.g.b 8
2624.2.g.c 16
2624.2.g.d 56
2624.2.i \(\chi_{2624}(337, \cdot)\) n/a 164 2
2624.2.l \(\chi_{2624}(2305, \cdot)\) n/a 164 2
2624.2.n \(\chi_{2624}(657, \cdot)\) n/a 160 2
2624.2.o \(\chi_{2624}(81, \cdot)\) n/a 164 2
2624.2.r \(\chi_{2624}(993, \cdot)\) n/a 168 2
2624.2.t \(\chi_{2624}(401, \cdot)\) n/a 164 2
2624.2.u \(\chi_{2624}(385, \cdot)\) n/a 328 4
2624.2.v \(\chi_{2624}(167, \cdot)\) None 0 4
2624.2.x \(\chi_{2624}(79, \cdot)\) n/a 328 4
2624.2.ba \(\chi_{2624}(73, \cdot)\) None 0 4
2624.2.bc \(\chi_{2624}(407, \cdot)\) None 0 4
2624.2.be \(\chi_{2624}(519, \cdot)\) None 0 4
2624.2.bf \(\chi_{2624}(329, \cdot)\) None 0 4
2624.2.bj \(\chi_{2624}(735, \cdot)\) n/a 336 4
2624.2.bk \(\chi_{2624}(191, \cdot)\) n/a 328 4
2624.2.bm \(\chi_{2624}(409, \cdot)\) None 0 4
2624.2.bo \(\chi_{2624}(9, \cdot)\) None 0 4
2624.2.bp \(\chi_{2624}(495, \cdot)\) n/a 328 4
2624.2.bs \(\chi_{2624}(55, \cdot)\) None 0 4
2624.2.bu \(\chi_{2624}(769, \cdot)\) n/a 328 4
2624.2.bw \(\chi_{2624}(1185, \cdot)\) n/a 336 4
2624.2.by \(\chi_{2624}(353, \cdot)\) n/a 336 4
2624.2.ca \(\chi_{2624}(219, \cdot)\) n/a 2672 8
2624.2.cd \(\chi_{2624}(173, \cdot)\) n/a 2672 8
2624.2.ce \(\chi_{2624}(245, \cdot)\) n/a 2672 8
2624.2.cf \(\chi_{2624}(165, \cdot)\) n/a 2560 8
2624.2.cg \(\chi_{2624}(355, \cdot)\) n/a 2672 8
2624.2.ch \(\chi_{2624}(331, \cdot)\) n/a 2672 8
2624.2.cm \(\chi_{2624}(237, \cdot)\) n/a 2672 8
2624.2.co \(\chi_{2624}(3, \cdot)\) n/a 2672 8
2624.2.cr \(\chi_{2624}(241, \cdot)\) n/a 656 8
2624.2.cs \(\chi_{2624}(33, \cdot)\) n/a 672 8
2624.2.cv \(\chi_{2624}(113, \cdot)\) n/a 656 8
2624.2.cw \(\chi_{2624}(305, \cdot)\) n/a 656 8
2624.2.cy \(\chi_{2624}(449, \cdot)\) n/a 656 8
2624.2.da \(\chi_{2624}(49, \cdot)\) n/a 656 8
2624.2.dd \(\chi_{2624}(135, \cdot)\) None 0 16
2624.2.df \(\chi_{2624}(15, \cdot)\) n/a 1312 16
2624.2.dg \(\chi_{2624}(169, \cdot)\) None 0 16
2624.2.di \(\chi_{2624}(199, \cdot)\) None 0 16
2624.2.dk \(\chi_{2624}(151, \cdot)\) None 0 16
2624.2.dm \(\chi_{2624}(25, \cdot)\) None 0 16
2624.2.do \(\chi_{2624}(63, \cdot)\) n/a 1312 16
2624.2.dp \(\chi_{2624}(95, \cdot)\) n/a 1344 16
2624.2.dt \(\chi_{2624}(57, \cdot)\) None 0 16
2624.2.du \(\chi_{2624}(121, \cdot)\) None 0 16
2624.2.dx \(\chi_{2624}(47, \cdot)\) n/a 1312 16
2624.2.dy \(\chi_{2624}(7, \cdot)\) None 0 16
2624.2.eb \(\chi_{2624}(259, \cdot)\) n/a 10688 32
2624.2.ed \(\chi_{2624}(5, \cdot)\) n/a 10688 32
2624.2.ei \(\chi_{2624}(67, \cdot)\) n/a 10688 32
2624.2.ej \(\chi_{2624}(11, \cdot)\) n/a 10688 32
2624.2.ek \(\chi_{2624}(37, \cdot)\) n/a 10688 32
2624.2.el \(\chi_{2624}(45, \cdot)\) n/a 10688 32
2624.2.em \(\chi_{2624}(197, \cdot)\) n/a 10688 32
2624.2.ep \(\chi_{2624}(275, \cdot)\) n/a 10688 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)\(^{\oplus 2}\)