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Properties

Label 1368.4
Level 1368
Weight 4
Dimension 68563
Nonzero newspaces 48
Sturm bound 414720
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(414720\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1368))\).

Total New Old
Modular forms 157248 69175 88073
Cusp forms 153792 68563 85229
Eisenstein series 3456 612 2844

Trace form

\( 68563 q - 46 q^{2} - 66 q^{3} - 26 q^{4} + 44 q^{5} - 32 q^{6} + 30 q^{7} - 106 q^{8} - 186 q^{9} + O(q^{10}) \) \( 68563 q - 46 q^{2} - 66 q^{3} - 26 q^{4} + 44 q^{5} - 32 q^{6} + 30 q^{7} - 106 q^{8} - 186 q^{9} - 322 q^{10} - 268 q^{11} - 284 q^{12} - 128 q^{13} - 346 q^{14} - 120 q^{15} - 322 q^{16} + 176 q^{17} + 168 q^{18} + 24 q^{19} + 800 q^{20} - 456 q^{21} + 1190 q^{22} - 546 q^{23} + 456 q^{24} - 126 q^{25} - 118 q^{26} - 648 q^{27} + 142 q^{28} - 246 q^{29} - 308 q^{30} - 80 q^{31} - 386 q^{32} + 794 q^{33} - 2818 q^{34} + 1950 q^{35} + 1460 q^{36} + 1002 q^{37} - 448 q^{38} + 408 q^{39} - 1674 q^{40} + 1736 q^{41} + 164 q^{42} + 3212 q^{43} + 2022 q^{44} - 892 q^{45} + 5230 q^{46} + 1644 q^{47} + 1520 q^{48} - 3224 q^{49} + 6182 q^{50} - 762 q^{51} + 3070 q^{52} - 3880 q^{53} - 1320 q^{54} - 3762 q^{55} - 5302 q^{56} - 1681 q^{57} - 9704 q^{58} - 8752 q^{59} - 1668 q^{60} + 3634 q^{61} + 976 q^{62} - 2440 q^{63} + 4246 q^{64} + 2074 q^{65} - 5072 q^{66} + 1248 q^{67} + 1272 q^{68} + 7420 q^{69} + 3030 q^{70} + 9040 q^{71} - 1980 q^{72} - 3093 q^{73} - 7570 q^{74} + 11686 q^{75} - 12312 q^{76} - 1422 q^{77} - 7964 q^{78} - 15584 q^{79} - 24294 q^{80} - 4018 q^{81} - 26880 q^{82} - 15824 q^{83} - 376 q^{84} - 2488 q^{85} + 4064 q^{86} - 14172 q^{87} + 2750 q^{88} - 3562 q^{89} - 3812 q^{90} + 15894 q^{91} + 19584 q^{92} - 7492 q^{93} + 19662 q^{94} + 29686 q^{95} + 7920 q^{96} + 18186 q^{97} + 20598 q^{98} + 27066 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1368))\)

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
1368.4.a \(\chi_{1368}(1, \cdot)\) 1368.4.a.a 2 1
1368.4.a.b 2
1368.4.a.c 2
1368.4.a.d 3
1368.4.a.e 3
1368.4.a.f 3
1368.4.a.g 4
1368.4.a.h 4
1368.4.a.i 4
1368.4.a.j 4
1368.4.a.k 5
1368.4.a.l 5
1368.4.a.m 5
1368.4.a.n 5
1368.4.a.o 8
1368.4.a.p 8
1368.4.d \(\chi_{1368}(647, \cdot)\) None 0 1
1368.4.e \(\chi_{1368}(379, \cdot)\) n/a 298 1
1368.4.f \(\chi_{1368}(1025, \cdot)\) 1368.4.f.a 30 1
1368.4.f.b 30
1368.4.g \(\chi_{1368}(685, \cdot)\) n/a 270 1
1368.4.j \(\chi_{1368}(1331, \cdot)\) n/a 216 1
1368.4.k \(\chi_{1368}(1063, \cdot)\) None 0 1
1368.4.p \(\chi_{1368}(341, \cdot)\) n/a 240 1
1368.4.q \(\chi_{1368}(457, \cdot)\) n/a 324 2
1368.4.r \(\chi_{1368}(49, \cdot)\) n/a 360 2
1368.4.s \(\chi_{1368}(505, \cdot)\) n/a 150 2
1368.4.t \(\chi_{1368}(121, \cdot)\) n/a 360 2
1368.4.w \(\chi_{1368}(277, \cdot)\) n/a 1432 2
1368.4.x \(\chi_{1368}(65, \cdot)\) n/a 360 2
1368.4.y \(\chi_{1368}(331, \cdot)\) n/a 1432 2
1368.4.z \(\chi_{1368}(311, \cdot)\) None 0 2
1368.4.be \(\chi_{1368}(487, \cdot)\) None 0 2
1368.4.bf \(\chi_{1368}(467, \cdot)\) n/a 480 2
1368.4.bi \(\chi_{1368}(797, \cdot)\) n/a 1432 2
1368.4.bl \(\chi_{1368}(293, \cdot)\) n/a 1432 2
1368.4.bm \(\chi_{1368}(103, \cdot)\) None 0 2
1368.4.bn \(\chi_{1368}(83, \cdot)\) n/a 1432 2
1368.4.bq \(\chi_{1368}(419, \cdot)\) n/a 1296 2
1368.4.br \(\chi_{1368}(151, \cdot)\) None 0 2
1368.4.bu \(\chi_{1368}(1133, \cdot)\) n/a 480 2
1368.4.bx \(\chi_{1368}(1171, \cdot)\) n/a 596 2
1368.4.by \(\chi_{1368}(1151, \cdot)\) None 0 2
1368.4.cb \(\chi_{1368}(349, \cdot)\) n/a 1432 2
1368.4.cc \(\chi_{1368}(977, \cdot)\) n/a 360 2
1368.4.cf \(\chi_{1368}(113, \cdot)\) n/a 360 2
1368.4.cg \(\chi_{1368}(229, \cdot)\) n/a 1296 2
1368.4.cl \(\chi_{1368}(191, \cdot)\) None 0 2
1368.4.cm \(\chi_{1368}(835, \cdot)\) n/a 1432 2
1368.4.cp \(\chi_{1368}(259, \cdot)\) n/a 1432 2
1368.4.cq \(\chi_{1368}(239, \cdot)\) None 0 2
1368.4.ct \(\chi_{1368}(1189, \cdot)\) n/a 596 2
1368.4.cu \(\chi_{1368}(449, \cdot)\) n/a 120 2
1368.4.cv \(\chi_{1368}(221, \cdot)\) n/a 1432 2
1368.4.da \(\chi_{1368}(31, \cdot)\) None 0 2
1368.4.db \(\chi_{1368}(11, \cdot)\) n/a 1432 2
1368.4.dc \(\chi_{1368}(73, \cdot)\) n/a 450 6
1368.4.dd \(\chi_{1368}(25, \cdot)\) n/a 1080 6
1368.4.de \(\chi_{1368}(169, \cdot)\) n/a 1080 6
1368.4.dg \(\chi_{1368}(67, \cdot)\) n/a 4296 6
1368.4.di \(\chi_{1368}(23, \cdot)\) None 0 6
1368.4.dj \(\chi_{1368}(79, \cdot)\) None 0 6
1368.4.dl \(\chi_{1368}(275, \cdot)\) n/a 4296 6
1368.4.dn \(\chi_{1368}(41, \cdot)\) n/a 1080 6
1368.4.dp \(\chi_{1368}(61, \cdot)\) n/a 4296 6
1368.4.dt \(\chi_{1368}(53, \cdot)\) n/a 1440 6
1368.4.du \(\chi_{1368}(253, \cdot)\) n/a 1788 6
1368.4.dw \(\chi_{1368}(89, \cdot)\) n/a 360 6
1368.4.dz \(\chi_{1368}(29, \cdot)\) n/a 4296 6
1368.4.eb \(\chi_{1368}(131, \cdot)\) n/a 4296 6
1368.4.ed \(\chi_{1368}(295, \cdot)\) None 0 6
1368.4.eg \(\chi_{1368}(91, \cdot)\) n/a 1788 6
1368.4.ei \(\chi_{1368}(215, \cdot)\) None 0 6
1368.4.ej \(\chi_{1368}(127, \cdot)\) None 0 6
1368.4.el \(\chi_{1368}(35, \cdot)\) n/a 1440 6
1368.4.eo \(\chi_{1368}(47, \cdot)\) None 0 6
1368.4.eq \(\chi_{1368}(211, \cdot)\) n/a 4296 6
1368.4.et \(\chi_{1368}(173, \cdot)\) n/a 4296 6
1368.4.eu \(\chi_{1368}(85, \cdot)\) n/a 4296 6
1368.4.ew \(\chi_{1368}(257, \cdot)\) n/a 1080 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1368))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)