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Properties

Label 1638.4
Level 1638
Weight 4
Dimension 54406
Nonzero newspaces 84
Sturm bound 580608
Trace bound 18

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Defining parameters

Level: \( N \) = \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(580608\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1638))\).

Total New Old
Modular forms 220032 54406 165626
Cusp forms 215424 54406 161018
Eisenstein series 4608 0 4608

Trace form

\( 54406 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 16 q^{7} - 80 q^{8} - 420 q^{9} + O(q^{10}) \) \( 54406 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 16 q^{7} - 80 q^{8} - 420 q^{9} + 60 q^{10} + 264 q^{11} + 96 q^{12} + 826 q^{13} + 1048 q^{14} + 840 q^{15} - 128 q^{16} - 1134 q^{17} - 48 q^{18} - 2344 q^{19} - 792 q^{20} - 1512 q^{21} - 1464 q^{22} - 2700 q^{23} - 288 q^{24} - 902 q^{25} - 500 q^{26} + 1584 q^{27} + 880 q^{28} + 10206 q^{29} + 3792 q^{30} + 6860 q^{31} + 256 q^{32} + 3396 q^{33} - 408 q^{34} - 1620 q^{35} - 1008 q^{36} - 7006 q^{37} - 6976 q^{38} - 9720 q^{39} - 480 q^{40} - 16854 q^{41} - 3504 q^{42} - 6100 q^{43} - 2928 q^{44} - 4632 q^{45} + 3600 q^{46} + 4284 q^{47} - 576 q^{48} + 12676 q^{49} + 9844 q^{50} + 4164 q^{51} + 3664 q^{52} + 2004 q^{53} + 2376 q^{54} - 1800 q^{55} + 352 q^{56} + 10092 q^{57} - 2076 q^{58} + 10188 q^{59} + 4320 q^{60} - 10114 q^{61} + 2528 q^{62} + 23628 q^{63} + 1408 q^{64} + 29514 q^{65} + 10752 q^{66} + 18104 q^{67} + 6456 q^{68} + 13104 q^{69} + 2832 q^{70} - 5808 q^{71} - 96 q^{72} - 7468 q^{73} + 4724 q^{74} - 27468 q^{75} + 6560 q^{76} - 15084 q^{77} - 8280 q^{78} - 18508 q^{79} - 2976 q^{80} - 13068 q^{81} - 14940 q^{82} - 32340 q^{83} + 1488 q^{84} - 35610 q^{85} + 2264 q^{86} - 888 q^{87} + 4704 q^{88} + 2316 q^{89} + 8448 q^{90} - 8870 q^{91} - 9504 q^{92} + 17976 q^{93} - 12720 q^{94} + 16788 q^{95} + 768 q^{96} + 5252 q^{97} - 26696 q^{98} - 56784 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1638))\)

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
1638.4.a \(\chi_{1638}(1, \cdot)\) 1638.4.a.a 1 1
1638.4.a.b 1
1638.4.a.c 1
1638.4.a.d 1
1638.4.a.e 1
1638.4.a.f 1
1638.4.a.g 1
1638.4.a.h 1
1638.4.a.i 1
1638.4.a.j 1
1638.4.a.k 1
1638.4.a.l 2
1638.4.a.m 2
1638.4.a.n 2
1638.4.a.o 2
1638.4.a.p 2
1638.4.a.q 2
1638.4.a.r 2
1638.4.a.s 2
1638.4.a.t 2
1638.4.a.u 2
1638.4.a.v 3
1638.4.a.w 3
1638.4.a.x 3
1638.4.a.y 3
1638.4.a.z 3
1638.4.a.ba 3
1638.4.a.bb 3
1638.4.a.bc 3
1638.4.a.bd 3
1638.4.a.be 4
1638.4.a.bf 4
1638.4.a.bg 4
1638.4.a.bh 5
1638.4.a.bi 5
1638.4.a.bj 5
1638.4.a.bk 5
1638.4.c \(\chi_{1638}(883, \cdot)\) n/a 104 1
1638.4.e \(\chi_{1638}(1637, \cdot)\) n/a 112 1
1638.4.g \(\chi_{1638}(755, \cdot)\) 1638.4.g.a 48 1
1638.4.g.b 48
1638.4.i \(\chi_{1638}(625, \cdot)\) n/a 576 2
1638.4.j \(\chi_{1638}(235, \cdot)\) n/a 240 2
1638.4.k \(\chi_{1638}(211, \cdot)\) n/a 504 2
1638.4.l \(\chi_{1638}(373, \cdot)\) n/a 672 2
1638.4.m \(\chi_{1638}(289, \cdot)\) n/a 280 2
1638.4.n \(\chi_{1638}(547, \cdot)\) n/a 432 2
1638.4.o \(\chi_{1638}(841, \cdot)\) n/a 504 2
1638.4.p \(\chi_{1638}(919, \cdot)\) n/a 280 2
1638.4.q \(\chi_{1638}(529, \cdot)\) n/a 672 2
1638.4.r \(\chi_{1638}(757, \cdot)\) n/a 212 2
1638.4.s \(\chi_{1638}(445, \cdot)\) n/a 672 2
1638.4.t \(\chi_{1638}(835, \cdot)\) n/a 672 2
1638.4.u \(\chi_{1638}(79, \cdot)\) n/a 576 2
1638.4.x \(\chi_{1638}(307, \cdot)\) n/a 280 2
1638.4.y \(\chi_{1638}(827, \cdot)\) n/a 168 2
1638.4.z \(\chi_{1638}(571, \cdot)\) n/a 672 2
1638.4.bc \(\chi_{1638}(251, \cdot)\) n/a 224 2
1638.4.bd \(\chi_{1638}(173, \cdot)\) n/a 672 2
1638.4.bg \(\chi_{1638}(563, \cdot)\) n/a 672 2
1638.4.bi \(\chi_{1638}(1213, \cdot)\) n/a 672 2
1638.4.bj \(\chi_{1638}(127, \cdot)\) n/a 208 2
1638.4.bm \(\chi_{1638}(205, \cdot)\) n/a 672 2
1638.4.bn \(\chi_{1638}(311, \cdot)\) n/a 672 2
1638.4.bq \(\chi_{1638}(971, \cdot)\) n/a 224 2
1638.4.br \(\chi_{1638}(965, \cdot)\) n/a 672 2
1638.4.bu \(\chi_{1638}(887, \cdot)\) n/a 672 2
1638.4.cd \(\chi_{1638}(731, \cdot)\) n/a 672 2
1638.4.ce \(\chi_{1638}(419, \cdot)\) n/a 672 2
1638.4.cf \(\chi_{1638}(521, \cdot)\) n/a 192 2
1638.4.cg \(\chi_{1638}(131, \cdot)\) n/a 576 2
1638.4.cl \(\chi_{1638}(209, \cdot)\) n/a 576 2
1638.4.cm \(\chi_{1638}(269, \cdot)\) n/a 224 2
1638.4.cr \(\chi_{1638}(361, \cdot)\) n/a 280 2
1638.4.cs \(\chi_{1638}(589, \cdot)\) n/a 504 2
1638.4.cv \(\chi_{1638}(277, \cdot)\) n/a 672 2
1638.4.cy \(\chi_{1638}(1343, \cdot)\) n/a 672 2
1638.4.cz \(\chi_{1638}(467, \cdot)\) n/a 224 2
1638.4.da \(\chi_{1638}(857, \cdot)\) n/a 672 2
1638.4.db \(\chi_{1638}(101, \cdot)\) n/a 672 2
1638.4.dg \(\chi_{1638}(17, \cdot)\) n/a 224 2
1638.4.dh \(\chi_{1638}(545, \cdot)\) n/a 672 2
1638.4.dk \(\chi_{1638}(121, \cdot)\) n/a 672 2
1638.4.dl \(\chi_{1638}(25, \cdot)\) n/a 672 2
1638.4.dm \(\chi_{1638}(415, \cdot)\) n/a 280 2
1638.4.dn \(\chi_{1638}(43, \cdot)\) n/a 504 2
1638.4.ds \(\chi_{1638}(337, \cdot)\) n/a 504 2
1638.4.dt \(\chi_{1638}(1297, \cdot)\) n/a 280 2
1638.4.dv \(\chi_{1638}(335, \cdot)\) n/a 672 2
1638.4.dw \(\chi_{1638}(647, \cdot)\) n/a 224 2
1638.4.dz \(\chi_{1638}(257, \cdot)\) n/a 672 2
1638.4.ea \(\chi_{1638}(677, \cdot)\) n/a 576 2
1638.4.eg \(\chi_{1638}(185, \cdot)\) n/a 672 2
1638.4.eh \(\chi_{1638}(503, \cdot)\) n/a 224 2
1638.4.ek \(\chi_{1638}(815, \cdot)\) n/a 672 2
1638.4.eu \(\chi_{1638}(31, \cdot)\) n/a 1344 4
1638.4.ev \(\chi_{1638}(97, \cdot)\) n/a 1344 4
1638.4.ew \(\chi_{1638}(115, \cdot)\) n/a 1344 4
1638.4.ex \(\chi_{1638}(695, \cdot)\) n/a 1344 4
1638.4.ey \(\chi_{1638}(71, \cdot)\) n/a 336 4
1638.4.ez \(\chi_{1638}(359, \cdot)\) n/a 448 4
1638.4.fa \(\chi_{1638}(617, \cdot)\) n/a 1008 4
1638.4.fb \(\chi_{1638}(431, \cdot)\) n/a 448 4
1638.4.fc \(\chi_{1638}(515, \cdot)\) n/a 1344 4
1638.4.fd \(\chi_{1638}(535, \cdot)\) n/a 1344 4
1638.4.fe \(\chi_{1638}(1189, \cdot)\) n/a 560 4
1638.4.ff \(\chi_{1638}(229, \cdot)\) n/a 1344 4
1638.4.fg \(\chi_{1638}(19, \cdot)\) n/a 560 4
1638.4.fh \(\chi_{1638}(73, \cdot)\) n/a 560 4
1638.4.fi \(\chi_{1638}(223, \cdot)\) n/a 1344 4
1638.4.fj \(\chi_{1638}(317, \cdot)\) n/a 1344 4
1638.4.fk \(\chi_{1638}(11, \cdot)\) n/a 1344 4
1638.4.fl \(\chi_{1638}(743, \cdot)\) n/a 1008 4
1638.4.ge \(\chi_{1638}(145, \cdot)\) n/a 560 4
1638.4.gf \(\chi_{1638}(821, \cdot)\) n/a 1344 4
1638.4.gg \(\chi_{1638}(137, \cdot)\) n/a 1344 4
1638.4.gh \(\chi_{1638}(239, \cdot)\) n/a 1008 4
1638.4.gi \(\chi_{1638}(409, \cdot)\) n/a 1344 4
1638.4.gj \(\chi_{1638}(241, \cdot)\) n/a 1344 4
1638.4.gk \(\chi_{1638}(265, \cdot)\) n/a 1344 4
1638.4.gl \(\chi_{1638}(305, \cdot)\) n/a 448 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1638))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1638)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(819))\)\(^{\oplus 2}\)