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Properties

Label 2912.2
Level 2912
Weight 2
Dimension 136348
Nonzero newspaces 100
Sturm bound 1032192
Trace bound 41

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Defining parameters

Level: \( N \) = \( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(1032192\)
Trace bound: \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2912))\).

Total New Old
Modular forms 262656 138548 124108
Cusp forms 253441 136348 117093
Eisenstein series 9215 2200 7015

Trace form

\( 136348 q - 160 q^{2} - 124 q^{3} - 160 q^{4} - 168 q^{5} - 160 q^{6} - 152 q^{7} - 400 q^{8} - 244 q^{9} + O(q^{10}) \) \( 136348 q - 160 q^{2} - 124 q^{3} - 160 q^{4} - 168 q^{5} - 160 q^{6} - 152 q^{7} - 400 q^{8} - 244 q^{9} - 128 q^{10} - 124 q^{11} - 96 q^{12} - 164 q^{13} - 408 q^{14} - 288 q^{15} - 80 q^{16} - 64 q^{17} - 80 q^{18} - 124 q^{19} - 96 q^{20} - 200 q^{21} - 352 q^{22} - 92 q^{23} - 208 q^{24} - 236 q^{25} - 216 q^{26} - 160 q^{27} - 240 q^{28} - 440 q^{29} - 288 q^{30} - 44 q^{31} - 240 q^{32} - 392 q^{33} - 208 q^{34} - 104 q^{35} - 512 q^{36} - 168 q^{37} - 128 q^{38} - 68 q^{39} - 304 q^{40} - 192 q^{41} - 160 q^{42} - 248 q^{43} + 8 q^{45} - 32 q^{46} - 36 q^{47} + 48 q^{48} - 28 q^{49} - 240 q^{50} + 4 q^{51} - 160 q^{52} - 136 q^{53} - 112 q^{54} - 168 q^{55} - 176 q^{56} - 400 q^{57} - 176 q^{58} - 156 q^{59} - 176 q^{60} + 24 q^{61} - 240 q^{62} - 120 q^{63} - 544 q^{64} - 412 q^{65} - 448 q^{66} - 212 q^{67} - 80 q^{68} + 64 q^{69} - 224 q^{70} - 408 q^{71} - 64 q^{72} - 256 q^{73} - 96 q^{74} - 40 q^{75} - 160 q^{76} - 168 q^{77} - 360 q^{78} - 252 q^{79} - 176 q^{80} - 108 q^{81} - 160 q^{82} + 48 q^{83} - 160 q^{84} - 288 q^{85} - 240 q^{86} + 280 q^{87} - 144 q^{88} - 400 q^{90} - 64 q^{91} - 1072 q^{92} + 80 q^{93} - 400 q^{94} + 284 q^{95} - 624 q^{96} - 320 q^{97} - 576 q^{98} + 168 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2912))\)

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
2912.2.a \(\chi_{2912}(1, \cdot)\) 2912.2.a.a 1 1
2912.2.a.b 1
2912.2.a.c 1
2912.2.a.d 1
2912.2.a.e 1
2912.2.a.f 1
2912.2.a.g 3
2912.2.a.h 3
2912.2.a.i 3
2912.2.a.j 3
2912.2.a.k 3
2912.2.a.l 3
2912.2.a.m 4
2912.2.a.n 4
2912.2.a.o 4
2912.2.a.p 4
2912.2.a.q 5
2912.2.a.r 5
2912.2.a.s 5
2912.2.a.t 5
2912.2.a.u 6
2912.2.a.v 6
2912.2.b \(\chi_{2912}(1455, \cdot)\) n/a 108 1
2912.2.c \(\chi_{2912}(1457, \cdot)\) 2912.2.c.a 34 1
2912.2.c.b 38
2912.2.h \(\chi_{2912}(2575, \cdot)\) 2912.2.h.a 48 1
2912.2.h.b 48
2912.2.i \(\chi_{2912}(337, \cdot)\) 2912.2.i.a 84 1
2912.2.j \(\chi_{2912}(1119, \cdot)\) 2912.2.j.a 48 1
2912.2.j.b 48
2912.2.k \(\chi_{2912}(1793, \cdot)\) 2912.2.k.a 2 1
2912.2.k.b 2
2912.2.k.c 4
2912.2.k.d 4
2912.2.k.e 4
2912.2.k.f 4
2912.2.k.g 8
2912.2.k.h 12
2912.2.k.i 14
2912.2.k.j 14
2912.2.k.k 16
2912.2.p \(\chi_{2912}(2911, \cdot)\) n/a 112 1
2912.2.q \(\chi_{2912}(289, \cdot)\) n/a 224 2
2912.2.r \(\chi_{2912}(417, \cdot)\) n/a 192 2
2912.2.s \(\chi_{2912}(1121, \cdot)\) n/a 168 2
2912.2.t \(\chi_{2912}(737, \cdot)\) n/a 224 2
2912.2.v \(\chi_{2912}(1695, \cdot)\) n/a 168 2
2912.2.w \(\chi_{2912}(993, \cdot)\) n/a 224 2
2912.2.y \(\chi_{2912}(1191, \cdot)\) None 0 2
2912.2.z \(\chi_{2912}(489, \cdot)\) None 0 2
2912.2.bd \(\chi_{2912}(391, \cdot)\) None 0 2
2912.2.be \(\chi_{2912}(1065, \cdot)\) None 0 2
2912.2.bh \(\chi_{2912}(727, \cdot)\) None 0 2
2912.2.bi \(\chi_{2912}(729, \cdot)\) None 0 2
2912.2.bm \(\chi_{2912}(967, \cdot)\) None 0 2
2912.2.bn \(\chi_{2912}(265, \cdot)\) None 0 2
2912.2.bp \(\chi_{2912}(239, \cdot)\) n/a 168 2
2912.2.bq \(\chi_{2912}(2449, \cdot)\) n/a 216 2
2912.2.bu \(\chi_{2912}(849, \cdot)\) n/a 216 2
2912.2.bv \(\chi_{2912}(367, \cdot)\) n/a 216 2
2912.2.bw \(\chi_{2912}(81, \cdot)\) n/a 216 2
2912.2.bx \(\chi_{2912}(719, \cdot)\) n/a 216 2
2912.2.cc \(\chi_{2912}(225, \cdot)\) n/a 168 2
2912.2.cd \(\chi_{2912}(2239, \cdot)\) n/a 224 2
2912.2.ce \(\chi_{2912}(927, \cdot)\) n/a 224 2
2912.2.cf \(\chi_{2912}(831, \cdot)\) n/a 224 2
2912.2.co \(\chi_{2912}(961, \cdot)\) n/a 224 2
2912.2.cp \(\chi_{2912}(703, \cdot)\) n/a 192 2
2912.2.cq \(\chi_{2912}(159, \cdot)\) n/a 224 2
2912.2.cr \(\chi_{2912}(641, \cdot)\) n/a 224 2
2912.2.cs \(\chi_{2912}(1343, \cdot)\) n/a 224 2
2912.2.cx \(\chi_{2912}(113, \cdot)\) n/a 168 2
2912.2.cy \(\chi_{2912}(335, \cdot)\) n/a 216 2
2912.2.cz \(\chi_{2912}(753, \cdot)\) n/a 216 2
2912.2.da \(\chi_{2912}(495, \cdot)\) n/a 192 2
2912.2.db \(\chi_{2912}(815, \cdot)\) n/a 216 2
2912.2.dc \(\chi_{2912}(1297, \cdot)\) n/a 216 2
2912.2.dl \(\chi_{2912}(1167, \cdot)\) n/a 216 2
2912.2.dm \(\chi_{2912}(529, \cdot)\) n/a 216 2
2912.2.dn \(\chi_{2912}(625, \cdot)\) n/a 192 2
2912.2.do \(\chi_{2912}(1039, \cdot)\) n/a 216 2
2912.2.dp \(\chi_{2912}(1681, \cdot)\) n/a 168 2
2912.2.dq \(\chi_{2912}(783, \cdot)\) n/a 216 2
2912.2.dv \(\chi_{2912}(1375, \cdot)\) n/a 224 2
2912.2.dw \(\chi_{2912}(1089, \cdot)\) n/a 224 2
2912.2.dx \(\chi_{2912}(607, \cdot)\) n/a 224 2
2912.2.eb \(\chi_{2912}(365, \cdot)\) n/a 1152 4
2912.2.ed \(\chi_{2912}(363, \cdot)\) n/a 1776 4
2912.2.ee \(\chi_{2912}(853, \cdot)\) n/a 1776 4
2912.2.eh \(\chi_{2912}(125, \cdot)\) n/a 1776 4
2912.2.ei \(\chi_{2912}(99, \cdot)\) n/a 1344 4
2912.2.el \(\chi_{2912}(827, \cdot)\) n/a 1344 4
2912.2.em \(\chi_{2912}(701, \cdot)\) n/a 1344 4
2912.2.eo \(\chi_{2912}(27, \cdot)\) n/a 1536 4
2912.2.er \(\chi_{2912}(33, \cdot)\) n/a 448 4
2912.2.es \(\chi_{2912}(1887, \cdot)\) n/a 448 4
2912.2.ev \(\chi_{2912}(1775, \cdot)\) n/a 432 4
2912.2.ey \(\chi_{2912}(657, \cdot)\) n/a 432 4
2912.2.ez \(\chi_{2912}(369, \cdot)\) n/a 432 4
2912.2.fa \(\chi_{2912}(15, \cdot)\) n/a 336 4
2912.2.fb \(\chi_{2912}(655, \cdot)\) n/a 432 4
2912.2.fe \(\chi_{2912}(145, \cdot)\) n/a 432 4
2912.2.fi \(\chi_{2912}(713, \cdot)\) None 0 4
2912.2.fj \(\chi_{2912}(1415, \cdot)\) None 0 4
2912.2.fm \(\chi_{2912}(201, \cdot)\) None 0 4
2912.2.fn \(\chi_{2912}(375, \cdot)\) None 0 4
2912.2.fo \(\chi_{2912}(487, \cdot)\) None 0 4
2912.2.fp \(\chi_{2912}(1097, \cdot)\) None 0 4
2912.2.fq \(\chi_{2912}(135, \cdot)\) None 0 4
2912.2.fr \(\chi_{2912}(89, \cdot)\) None 0 4
2912.2.fx \(\chi_{2912}(9, \cdot)\) None 0 4
2912.2.fy \(\chi_{2912}(647, \cdot)\) None 0 4
2912.2.gb \(\chi_{2912}(121, \cdot)\) None 0 4
2912.2.gc \(\chi_{2912}(1095, \cdot)\) None 0 4
2912.2.gf \(\chi_{2912}(25, \cdot)\) None 0 4
2912.2.gg \(\chi_{2912}(1223, \cdot)\) None 0 4
2912.2.gj \(\chi_{2912}(199, \cdot)\) None 0 4
2912.2.gl \(\chi_{2912}(393, \cdot)\) None 0 4
2912.2.gm \(\chi_{2912}(615, \cdot)\) None 0 4
2912.2.go \(\chi_{2912}(1017, \cdot)\) None 0 4
2912.2.gr \(\chi_{2912}(87, \cdot)\) None 0 4
2912.2.gt \(\chi_{2912}(953, \cdot)\) None 0 4
2912.2.gu \(\chi_{2912}(55, \cdot)\) None 0 4
2912.2.gw \(\chi_{2912}(569, \cdot)\) None 0 4
2912.2.gz \(\chi_{2912}(1145, \cdot)\) None 0 4
2912.2.ha \(\chi_{2912}(103, \cdot)\) None 0 4
2912.2.hc \(\chi_{2912}(297, \cdot)\) None 0 4
2912.2.hd \(\chi_{2912}(695, \cdot)\) None 0 4
2912.2.hk \(\chi_{2912}(583, \cdot)\) None 0 4
2912.2.hl \(\chi_{2912}(73, \cdot)\) None 0 4
2912.2.hm \(\chi_{2912}(359, \cdot)\) None 0 4
2912.2.hn \(\chi_{2912}(409, \cdot)\) None 0 4
2912.2.ho \(\chi_{2912}(41, \cdot)\) None 0 4
2912.2.hp \(\chi_{2912}(71, \cdot)\) None 0 4
2912.2.ht \(\chi_{2912}(319, \cdot)\) n/a 448 4
2912.2.hw \(\chi_{2912}(97, \cdot)\) n/a 448 4
2912.2.hx \(\chi_{2912}(577, \cdot)\) n/a 448 4
2912.2.hy \(\chi_{2912}(799, \cdot)\) n/a 336 4
2912.2.hz \(\chi_{2912}(863, \cdot)\) n/a 448 4
2912.2.ic \(\chi_{2912}(1601, \cdot)\) n/a 448 4
2912.2.if \(\chi_{2912}(1489, \cdot)\) n/a 432 4
2912.2.ig \(\chi_{2912}(431, \cdot)\) n/a 432 4
2912.2.ii \(\chi_{2912}(467, \cdot)\) n/a 3552 8
2912.2.ik \(\chi_{2912}(53, \cdot)\) n/a 3072 8
2912.2.in \(\chi_{2912}(205, \cdot)\) n/a 3552 8
2912.2.io \(\chi_{2912}(3, \cdot)\) n/a 3552 8
2912.2.ir \(\chi_{2912}(139, \cdot)\) n/a 3552 8
2912.2.it \(\chi_{2912}(309, \cdot)\) n/a 2688 8
2912.2.iu \(\chi_{2912}(485, \cdot)\) n/a 3552 8
2912.2.ix \(\chi_{2912}(451, \cdot)\) n/a 3552 8
2912.2.iy \(\chi_{2912}(605, \cdot)\) n/a 3552 8
2912.2.jb \(\chi_{2912}(45, \cdot)\) n/a 3552 8
2912.2.jc \(\chi_{2912}(515, \cdot)\) n/a 3552 8
2912.2.je \(\chi_{2912}(267, \cdot)\) n/a 2688 8
2912.2.jf \(\chi_{2912}(11, \cdot)\) n/a 3552 8
2912.2.jk \(\chi_{2912}(163, \cdot)\) n/a 3552 8
2912.2.jl \(\chi_{2912}(323, \cdot)\) n/a 2688 8
2912.2.jn \(\chi_{2912}(291, \cdot)\) n/a 3552 8
2912.2.jo \(\chi_{2912}(229, \cdot)\) n/a 3552 8
2912.2.jq \(\chi_{2912}(349, \cdot)\) n/a 3552 8
2912.2.jr \(\chi_{2912}(397, \cdot)\) n/a 3552 8
2912.2.jw \(\chi_{2912}(661, \cdot)\) n/a 3552 8
2912.2.jx \(\chi_{2912}(293, \cdot)\) n/a 3552 8
2912.2.jz \(\chi_{2912}(5, \cdot)\) n/a 3552 8
2912.2.ka \(\chi_{2912}(219, \cdot)\) n/a 3552 8
2912.2.kd \(\chi_{2912}(123, \cdot)\) n/a 3552 8
2912.2.ke \(\chi_{2912}(165, \cdot)\) n/a 3552 8
2912.2.kg \(\chi_{2912}(251, \cdot)\) n/a 3552 8
2912.2.kj \(\chi_{2912}(283, \cdot)\) n/a 3552 8
2912.2.kl \(\chi_{2912}(373, \cdot)\) n/a 3552 8
2912.2.km \(\chi_{2912}(29, \cdot)\) n/a 2688 8
2912.2.ko \(\chi_{2912}(75, \cdot)\) n/a 3552 8
2912.2.kr \(\chi_{2912}(131, \cdot)\) n/a 3072 8
2912.2.kt \(\chi_{2912}(389, \cdot)\) n/a 3552 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2912))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2912)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2912))\)\(^{\oplus 1}\)