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Properties

Label 3040.2
Level 3040
Weight 2
Dimension 140748
Nonzero newspaces 60
Sturm bound 1105920
Trace bound 77

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Defining parameters

Level: \( N \) = \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1105920\)
Trace bound: \(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3040))\).

Total New Old
Modular forms 281088 142788 138300
Cusp forms 271873 140748 131125
Eisenstein series 9215 2040 7175

Trace form

\( 140748 q - 128 q^{2} - 100 q^{3} - 128 q^{4} - 196 q^{5} - 384 q^{6} - 100 q^{7} - 128 q^{8} - 196 q^{9} + O(q^{10}) \) \( 140748 q - 128 q^{2} - 100 q^{3} - 128 q^{4} - 196 q^{5} - 384 q^{6} - 100 q^{7} - 128 q^{8} - 196 q^{9} - 176 q^{10} - 292 q^{11} - 64 q^{12} - 104 q^{13} - 64 q^{14} - 138 q^{15} - 304 q^{16} - 48 q^{17} - 48 q^{18} - 100 q^{19} - 376 q^{20} - 384 q^{21} - 80 q^{22} - 68 q^{23} - 176 q^{24} - 296 q^{25} - 464 q^{26} + 20 q^{27} - 208 q^{28} - 152 q^{29} - 256 q^{30} - 180 q^{31} - 208 q^{32} - 248 q^{33} - 176 q^{34} - 50 q^{35} - 496 q^{36} - 56 q^{37} - 120 q^{38} - 56 q^{39} - 168 q^{40} - 464 q^{41} - 48 q^{42} - 4 q^{43} + 32 q^{44} - 76 q^{45} - 256 q^{46} - 36 q^{47} + 80 q^{48} - 20 q^{49} - 112 q^{50} - 276 q^{51} - 96 q^{52} + 8 q^{53} - 80 q^{54} - 170 q^{55} - 336 q^{56} - 224 q^{57} - 288 q^{58} - 220 q^{59} - 328 q^{60} - 296 q^{61} - 208 q^{62} - 308 q^{63} - 368 q^{64} - 564 q^{65} - 736 q^{66} - 308 q^{67} - 272 q^{68} - 192 q^{69} - 504 q^{70} - 484 q^{71} - 512 q^{72} - 336 q^{73} - 416 q^{74} - 304 q^{75} - 536 q^{76} - 400 q^{77} - 576 q^{78} - 204 q^{79} - 520 q^{80} - 404 q^{81} - 448 q^{82} - 20 q^{83} - 656 q^{84} - 352 q^{85} - 720 q^{86} + 36 q^{87} - 464 q^{88} - 272 q^{89} - 648 q^{90} - 164 q^{91} - 560 q^{92} - 368 q^{93} - 304 q^{94} - 98 q^{95} - 1056 q^{96} - 304 q^{97} - 304 q^{98} + 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3040))\)

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
3040.2.a \(\chi_{3040}(1, \cdot)\) 3040.2.a.a 1 1
3040.2.a.b 1
3040.2.a.c 1
3040.2.a.d 1
3040.2.a.e 2
3040.2.a.f 2
3040.2.a.g 2
3040.2.a.h 2
3040.2.a.i 3
3040.2.a.j 3
3040.2.a.k 3
3040.2.a.l 3
3040.2.a.m 3
3040.2.a.n 3
3040.2.a.o 3
3040.2.a.p 3
3040.2.a.q 4
3040.2.a.r 4
3040.2.a.s 4
3040.2.a.t 4
3040.2.a.u 5
3040.2.a.v 5
3040.2.a.w 5
3040.2.a.x 5
3040.2.d \(\chi_{3040}(609, \cdot)\) n/a 108 1
3040.2.e \(\chi_{3040}(911, \cdot)\) 3040.2.e.a 80 1
3040.2.f \(\chi_{3040}(1521, \cdot)\) 3040.2.f.a 28 1
3040.2.f.b 44
3040.2.g \(\chi_{3040}(3039, \cdot)\) n/a 120 1
3040.2.j \(\chi_{3040}(2431, \cdot)\) 3040.2.j.a 4 1
3040.2.j.b 4
3040.2.j.c 4
3040.2.j.d 8
3040.2.j.e 20
3040.2.j.f 40
3040.2.k \(\chi_{3040}(2129, \cdot)\) n/a 108 1
3040.2.p \(\chi_{3040}(1519, \cdot)\) n/a 116 1
3040.2.q \(\chi_{3040}(961, \cdot)\) n/a 160 2
3040.2.r \(\chi_{3040}(2393, \cdot)\) None 0 2
3040.2.t \(\chi_{3040}(1863, \cdot)\) None 0 2
3040.2.w \(\chi_{3040}(759, \cdot)\) None 0 2
3040.2.y \(\chi_{3040}(761, \cdot)\) None 0 2
3040.2.bb \(\chi_{3040}(113, \cdot)\) n/a 232 2
3040.2.bc \(\chi_{3040}(1407, \cdot)\) n/a 216 2
3040.2.bd \(\chi_{3040}(417, \cdot)\) n/a 240 2
3040.2.be \(\chi_{3040}(1103, \cdot)\) n/a 216 2
3040.2.bi \(\chi_{3040}(1369, \cdot)\) None 0 2
3040.2.bk \(\chi_{3040}(151, \cdot)\) None 0 2
3040.2.bl \(\chi_{3040}(343, \cdot)\) None 0 2
3040.2.bn \(\chi_{3040}(873, \cdot)\) None 0 2
3040.2.bp \(\chi_{3040}(49, \cdot)\) n/a 232 2
3040.2.bq \(\chi_{3040}(31, \cdot)\) n/a 160 2
3040.2.bv \(\chi_{3040}(559, \cdot)\) n/a 232 2
3040.2.by \(\chi_{3040}(1551, \cdot)\) n/a 160 2
3040.2.bz \(\chi_{3040}(1569, \cdot)\) n/a 240 2
3040.2.ca \(\chi_{3040}(639, \cdot)\) n/a 240 2
3040.2.cb \(\chi_{3040}(881, \cdot)\) n/a 160 2
3040.2.ce \(\chi_{3040}(37, \cdot)\) n/a 1904 4
3040.2.cf \(\chi_{3040}(1027, \cdot)\) n/a 1728 4
3040.2.ck \(\chi_{3040}(531, \cdot)\) n/a 1280 4
3040.2.cl \(\chi_{3040}(381, \cdot)\) n/a 1152 4
3040.2.co \(\chi_{3040}(229, \cdot)\) n/a 1728 4
3040.2.cp \(\chi_{3040}(379, \cdot)\) n/a 1904 4
3040.2.cq \(\chi_{3040}(267, \cdot)\) n/a 1728 4
3040.2.cr \(\chi_{3040}(797, \cdot)\) n/a 1904 4
3040.2.cu \(\chi_{3040}(161, \cdot)\) n/a 480 6
3040.2.cv \(\chi_{3040}(217, \cdot)\) None 0 4
3040.2.cx \(\chi_{3040}(7, \cdot)\) None 0 4
3040.2.da \(\chi_{3040}(121, \cdot)\) None 0 4
3040.2.dc \(\chi_{3040}(1319, \cdot)\) None 0 4
3040.2.dd \(\chi_{3040}(753, \cdot)\) n/a 464 4
3040.2.de \(\chi_{3040}(543, \cdot)\) n/a 480 4
3040.2.dj \(\chi_{3040}(673, \cdot)\) n/a 480 4
3040.2.dk \(\chi_{3040}(463, \cdot)\) n/a 464 4
3040.2.dm \(\chi_{3040}(711, \cdot)\) None 0 4
3040.2.do \(\chi_{3040}(729, \cdot)\) None 0 4
3040.2.dp \(\chi_{3040}(87, \cdot)\) None 0 4
3040.2.dr \(\chi_{3040}(297, \cdot)\) None 0 4
3040.2.dt \(\chi_{3040}(79, \cdot)\) n/a 696 6
3040.2.dy \(\chi_{3040}(81, \cdot)\) n/a 480 6
3040.2.dz \(\chi_{3040}(319, \cdot)\) n/a 720 6
3040.2.ec \(\chi_{3040}(289, \cdot)\) n/a 720 6
3040.2.ed \(\chi_{3040}(431, \cdot)\) n/a 480 6
3040.2.ee \(\chi_{3040}(831, \cdot)\) n/a 480 6
3040.2.ef \(\chi_{3040}(529, \cdot)\) n/a 696 6
3040.2.ei \(\chi_{3040}(387, \cdot)\) n/a 3808 8
3040.2.ej \(\chi_{3040}(597, \cdot)\) n/a 3808 8
3040.2.eo \(\chi_{3040}(179, \cdot)\) n/a 3808 8
3040.2.ep \(\chi_{3040}(349, \cdot)\) n/a 3808 8
3040.2.es \(\chi_{3040}(501, \cdot)\) n/a 2560 8
3040.2.et \(\chi_{3040}(331, \cdot)\) n/a 2560 8
3040.2.eu \(\chi_{3040}(293, \cdot)\) n/a 3808 8
3040.2.ev \(\chi_{3040}(83, \cdot)\) n/a 3808 8
3040.2.ey \(\chi_{3040}(9, \cdot)\) None 0 12
3040.2.ez \(\chi_{3040}(71, \cdot)\) None 0 12
3040.2.fe \(\chi_{3040}(33, \cdot)\) n/a 1440 12
3040.2.ff \(\chi_{3040}(47, \cdot)\) n/a 1392 12
3040.2.fi \(\chi_{3040}(23, \cdot)\) None 0 12
3040.2.fj \(\chi_{3040}(393, \cdot)\) None 0 12
3040.2.fm \(\chi_{3040}(793, \cdot)\) None 0 12
3040.2.fn \(\chi_{3040}(263, \cdot)\) None 0 12
3040.2.fq \(\chi_{3040}(337, \cdot)\) n/a 1392 12
3040.2.fr \(\chi_{3040}(63, \cdot)\) n/a 1440 12
3040.2.fs \(\chi_{3040}(441, \cdot)\) None 0 12
3040.2.ft \(\chi_{3040}(279, \cdot)\) None 0 12
3040.2.fy \(\chi_{3040}(53, \cdot)\) n/a 11424 24
3040.2.fz \(\chi_{3040}(187, \cdot)\) n/a 11424 24
3040.2.ga \(\chi_{3040}(61, \cdot)\) n/a 7680 24
3040.2.gb \(\chi_{3040}(59, \cdot)\) n/a 11424 24
3040.2.gc \(\chi_{3040}(149, \cdot)\) n/a 11424 24
3040.2.gd \(\chi_{3040}(51, \cdot)\) n/a 7680 24
3040.2.gk \(\chi_{3040}(43, \cdot)\) n/a 11424 24
3040.2.gl \(\chi_{3040}(13, \cdot)\) n/a 11424 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3040))\)\(^{\oplus 1}\)