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Properties

Label 3100.3
Level 3100
Weight 3
Dimension 307846
Nonzero newspaces 84
Sturm bound 1728000
Trace bound 23

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Defining parameters

Level: \( N \) = \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1728000\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(3100))\).

Total New Old
Modular forms 580200 310222 269978
Cusp forms 571800 307846 263954
Eisenstein series 8400 2376 6024

Trace form

\( 307846 q - 183 q^{2} + 8 q^{3} - 191 q^{4} - 460 q^{5} - 343 q^{6} - 56 q^{7} - 207 q^{8} - 382 q^{9} + O(q^{10}) \) \( 307846 q - 183 q^{2} + 8 q^{3} - 191 q^{4} - 460 q^{5} - 343 q^{6} - 56 q^{7} - 207 q^{8} - 382 q^{9} - 208 q^{10} + 80 q^{11} - 15 q^{12} - 342 q^{13} + 49 q^{14} + 4 q^{15} - 87 q^{16} - 578 q^{17} - 87 q^{18} - 200 q^{19} - 308 q^{20} - 713 q^{21} - 495 q^{22} - 119 q^{23} - 731 q^{24} - 296 q^{25} - 991 q^{26} + 443 q^{27} - 335 q^{28} + 8 q^{29} - 140 q^{30} + 54 q^{31} + 142 q^{32} + 320 q^{33} + 449 q^{34} + 416 q^{35} + 345 q^{36} - 217 q^{37} + 805 q^{38} + 485 q^{39} + 632 q^{40} - 611 q^{41} + 745 q^{42} + 295 q^{43} + 205 q^{44} - 240 q^{45} - 463 q^{46} - 152 q^{47} - 500 q^{48} - 1342 q^{49} - 228 q^{50} - 1124 q^{51} - 1166 q^{52} - 1710 q^{53} - 2182 q^{54} - 600 q^{55} - 1218 q^{56} - 2054 q^{57} - 1894 q^{58} - 1160 q^{59} - 2340 q^{60} - 1028 q^{61} - 905 q^{62} - 1588 q^{63} - 1061 q^{64} - 1000 q^{65} + 590 q^{66} - 436 q^{67} + 16 q^{68} + 1558 q^{69} - 380 q^{70} + 1144 q^{71} + 1172 q^{72} + 1378 q^{73} + 4 q^{74} + 36 q^{75} + 310 q^{76} + 1685 q^{77} + 90 q^{78} + 855 q^{79} - 508 q^{80} + 494 q^{81} - 1071 q^{82} + 2341 q^{83} - 2447 q^{84} + 1936 q^{85} - 943 q^{86} + 2496 q^{87} - 2175 q^{88} + 1963 q^{89} - 3148 q^{90} + 377 q^{91} - 2070 q^{92} - 436 q^{93} - 2386 q^{94} + 448 q^{95} - 1768 q^{96} - 587 q^{97} + 33 q^{98} - 525 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(3100))\)

We only show spaces with odd 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
3100.3.b \(\chi_{3100}(1551, \cdot)\) n/a 570 1
3100.3.d \(\chi_{3100}(1301, \cdot)\) 3100.3.d.a 2 1
3100.3.d.b 4
3100.3.d.c 4
3100.3.d.d 4
3100.3.d.e 20
3100.3.d.f 22
3100.3.d.g 22
3100.3.d.h 24
3100.3.f \(\chi_{3100}(1549, \cdot)\) 3100.3.f.a 4 1
3100.3.f.b 8
3100.3.f.c 40
3100.3.f.d 44
3100.3.h \(\chi_{3100}(1799, \cdot)\) n/a 540 1
3100.3.l \(\chi_{3100}(993, \cdot)\) n/a 180 2
3100.3.m \(\chi_{3100}(743, \cdot)\) n/a 1144 2
3100.3.t \(\chi_{3100}(1699, \cdot)\) n/a 1144 2
3100.3.v \(\chi_{3100}(1049, \cdot)\) n/a 192 2
3100.3.x \(\chi_{3100}(801, \cdot)\) n/a 202 2
3100.3.z \(\chi_{3100}(1451, \cdot)\) n/a 1204 2
3100.3.ba \(\chi_{3100}(1021, \cdot)\) n/a 640 4
3100.3.bc \(\chi_{3100}(411, \cdot)\) n/a 3824 4
3100.3.bf \(\chi_{3100}(309, \cdot)\) n/a 640 4
3100.3.bg \(\chi_{3100}(779, \cdot)\) n/a 3824 4
3100.3.bh \(\chi_{3100}(1399, \cdot)\) n/a 2288 4
3100.3.bi \(\chi_{3100}(1039, \cdot)\) n/a 3824 4
3100.3.bj \(\chi_{3100}(219, \cdot)\) n/a 3824 4
3100.3.bo \(\chi_{3100}(89, \cdot)\) n/a 640 4
3100.3.bp \(\chi_{3100}(829, \cdot)\) n/a 640 4
3100.3.bq \(\chi_{3100}(449, \cdot)\) n/a 384 4
3100.3.br \(\chi_{3100}(1329, \cdot)\) n/a 640 4
3100.3.bs \(\chi_{3100}(559, \cdot)\) n/a 3600 4
3100.3.bu \(\chi_{3100}(311, \cdot)\) n/a 3600 4
3100.3.bz \(\chi_{3100}(581, \cdot)\) n/a 640 4
3100.3.ca \(\chi_{3100}(461, \cdot)\) n/a 640 4
3100.3.cb \(\chi_{3100}(201, \cdot)\) n/a 408 4
3100.3.cc \(\chi_{3100}(1081, \cdot)\) n/a 640 4
3100.3.ch \(\chi_{3100}(531, \cdot)\) n/a 3824 4
3100.3.ci \(\chi_{3100}(1151, \cdot)\) n/a 2408 4
3100.3.cj \(\chi_{3100}(171, \cdot)\) n/a 3824 4
3100.3.ck \(\chi_{3100}(791, \cdot)\) n/a 3824 4
3100.3.cm \(\chi_{3100}(61, \cdot)\) n/a 640 4
3100.3.cn \(\chi_{3100}(39, \cdot)\) n/a 3824 4
3100.3.co \(\chi_{3100}(29, \cdot)\) n/a 640 4
3100.3.cq \(\chi_{3100}(243, \cdot)\) n/a 2288 4
3100.3.cr \(\chi_{3100}(893, \cdot)\) n/a 384 4
3100.3.dc \(\chi_{3100}(233, \cdot)\) n/a 1280 8
3100.3.dd \(\chi_{3100}(23, \cdot)\) n/a 7648 8
3100.3.de \(\chi_{3100}(27, \cdot)\) n/a 7648 8
3100.3.df \(\chi_{3100}(123, \cdot)\) n/a 7648 8
3100.3.dg \(\chi_{3100}(643, \cdot)\) n/a 4576 8
3100.3.dh \(\chi_{3100}(263, \cdot)\) n/a 7648 8
3100.3.di \(\chi_{3100}(147, \cdot)\) n/a 7648 8
3100.3.dj \(\chi_{3100}(373, \cdot)\) n/a 1200 8
3100.3.dk \(\chi_{3100}(97, \cdot)\) n/a 1280 8
3100.3.dl \(\chi_{3100}(157, \cdot)\) n/a 768 8
3100.3.dm \(\chi_{3100}(597, \cdot)\) n/a 1280 8
3100.3.dn \(\chi_{3100}(33, \cdot)\) n/a 1280 8
3100.3.dz \(\chi_{3100}(229, \cdot)\) n/a 1280 8
3100.3.ea \(\chi_{3100}(939, \cdot)\) n/a 7648 8
3100.3.eb \(\chi_{3100}(161, \cdot)\) n/a 1280 8
3100.3.ed \(\chi_{3100}(231, \cdot)\) n/a 7648 8
3100.3.ee \(\chi_{3100}(691, \cdot)\) n/a 7648 8
3100.3.ef \(\chi_{3100}(51, \cdot)\) n/a 4816 8
3100.3.eg \(\chi_{3100}(71, \cdot)\) n/a 7648 8
3100.3.el \(\chi_{3100}(261, \cdot)\) n/a 1280 8
3100.3.em \(\chi_{3100}(301, \cdot)\) n/a 808 8
3100.3.en \(\chi_{3100}(141, \cdot)\) n/a 1280 8
3100.3.eo \(\chi_{3100}(321, \cdot)\) n/a 1280 8
3100.3.et \(\chi_{3100}(191, \cdot)\) n/a 7648 8
3100.3.ev \(\chi_{3100}(439, \cdot)\) n/a 7648 8
3100.3.ew \(\chi_{3100}(509, \cdot)\) n/a 1280 8
3100.3.ex \(\chi_{3100}(549, \cdot)\) n/a 768 8
3100.3.ey \(\chi_{3100}(189, \cdot)\) n/a 1280 8
3100.3.ez \(\chi_{3100}(269, \cdot)\) n/a 1280 8
3100.3.fe \(\chi_{3100}(19, \cdot)\) n/a 7648 8
3100.3.ff \(\chi_{3100}(479, \cdot)\) n/a 7648 8
3100.3.fg \(\chi_{3100}(299, \cdot)\) n/a 4576 8
3100.3.fh \(\chi_{3100}(59, \cdot)\) n/a 7648 8
3100.3.fi \(\chi_{3100}(409, \cdot)\) n/a 1280 8
3100.3.fl \(\chi_{3100}(431, \cdot)\) n/a 7648 8
3100.3.fn \(\chi_{3100}(21, \cdot)\) n/a 1280 8
3100.3.fy \(\chi_{3100}(297, \cdot)\) n/a 2560 16
3100.3.fz \(\chi_{3100}(173, \cdot)\) n/a 2560 16
3100.3.ga \(\chi_{3100}(193, \cdot)\) n/a 1536 16
3100.3.gb \(\chi_{3100}(133, \cdot)\) n/a 2560 16
3100.3.gc \(\chi_{3100}(253, \cdot)\) n/a 2560 16
3100.3.gd \(\chi_{3100}(127, \cdot)\) n/a 15296 16
3100.3.ge \(\chi_{3100}(303, \cdot)\) n/a 15296 16
3100.3.gf \(\chi_{3100}(43, \cdot)\) n/a 9152 16
3100.3.gg \(\chi_{3100}(223, \cdot)\) n/a 15296 16
3100.3.gh \(\chi_{3100}(3, \cdot)\) n/a 15296 16
3100.3.gi \(\chi_{3100}(327, \cdot)\) n/a 15296 16
3100.3.gj \(\chi_{3100}(113, \cdot)\) n/a 2560 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(3100))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(3100)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1550))\)\(^{\oplus 2}\)