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Properties

Label 1116.2
Level 1116
Weight 2
Dimension 15664
Nonzero newspaces 40
Sturm bound 138240
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(138240\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1116))\).

Total New Old
Modular forms 35760 16188 19572
Cusp forms 33361 15664 17697
Eisenstein series 2399 524 1875

Trace form

\( 15664 q - 39 q^{2} - 35 q^{4} - 72 q^{5} - 54 q^{6} + 6 q^{7} - 45 q^{8} - 96 q^{9} + O(q^{10}) \) \( 15664 q - 39 q^{2} - 35 q^{4} - 72 q^{5} - 54 q^{6} + 6 q^{7} - 45 q^{8} - 96 q^{9} - 127 q^{10} + 6 q^{11} - 72 q^{12} - 76 q^{13} - 69 q^{14} - 18 q^{15} - 59 q^{16} - 114 q^{17} - 96 q^{18} - 81 q^{20} - 114 q^{21} - 51 q^{22} - 21 q^{23} - 66 q^{24} - 107 q^{25} - 45 q^{26} - 111 q^{28} - 126 q^{29} - 24 q^{30} - 21 q^{31} - 24 q^{32} - 150 q^{33} - 19 q^{34} - 18 q^{35} + 6 q^{36} - 295 q^{37} + 9 q^{38} + 6 q^{39} - 49 q^{40} - 147 q^{41} - 24 q^{42} - 23 q^{43} - 45 q^{44} - 150 q^{45} - 159 q^{46} - 18 q^{47} - 102 q^{48} - 98 q^{49} - 12 q^{50} - 34 q^{52} - 36 q^{53} - 138 q^{54} + 24 q^{55} + 54 q^{56} - 132 q^{57} - 4 q^{58} + 24 q^{59} - 72 q^{60} + 20 q^{61} + 45 q^{62} + 6 q^{63} - 65 q^{64} + 54 q^{65} - 12 q^{66} + 48 q^{67} + 90 q^{68} - 42 q^{69} + 102 q^{70} + 108 q^{71} - 18 q^{72} - 124 q^{73} + 90 q^{74} + 54 q^{75} + 36 q^{76} + 129 q^{77} - 36 q^{78} + 135 q^{79} - 45 q^{80} + 24 q^{81} - 163 q^{82} + 297 q^{83} - 120 q^{84} + 70 q^{85} - 87 q^{86} + 138 q^{87} - 3 q^{88} + 111 q^{89} - 72 q^{90} + 207 q^{91} - 138 q^{92} + 75 q^{93} - 54 q^{94} + 336 q^{95} - 84 q^{96} + 59 q^{97} - 45 q^{98} + 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1116))\)

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
1116.2.a \(\chi_{1116}(1, \cdot)\) 1116.2.a.a 1 1
1116.2.a.b 1
1116.2.a.c 1
1116.2.a.d 1
1116.2.a.e 1
1116.2.a.f 1
1116.2.a.g 2
1116.2.a.h 2
1116.2.a.i 2
1116.2.c \(\chi_{1116}(683, \cdot)\) 1116.2.c.a 60 1
1116.2.e \(\chi_{1116}(557, \cdot)\) 1116.2.e.a 12 1
1116.2.g \(\chi_{1116}(991, \cdot)\) 1116.2.g.a 4 1
1116.2.g.b 4
1116.2.g.c 4
1116.2.g.d 4
1116.2.g.e 4
1116.2.g.f 6
1116.2.g.g 8
1116.2.g.h 12
1116.2.g.i 16
1116.2.g.j 16
1116.2.i \(\chi_{1116}(253, \cdot)\) 1116.2.i.a 2 2
1116.2.i.b 2
1116.2.i.c 2
1116.2.i.d 4
1116.2.i.e 4
1116.2.i.f 6
1116.2.i.g 6
1116.2.j \(\chi_{1116}(373, \cdot)\) 1116.2.j.a 4 2
1116.2.j.b 26
1116.2.j.c 30
1116.2.k \(\chi_{1116}(769, \cdot)\) 1116.2.k.a 2 2
1116.2.k.b 62
1116.2.l \(\chi_{1116}(25, \cdot)\) 1116.2.l.a 2 2
1116.2.l.b 62
1116.2.m \(\chi_{1116}(109, \cdot)\) 1116.2.m.a 4 4
1116.2.m.b 4
1116.2.m.c 4
1116.2.m.d 8
1116.2.m.e 8
1116.2.m.f 12
1116.2.m.g 16
1116.2.n \(\chi_{1116}(335, \cdot)\) n/a 376 2
1116.2.p \(\chi_{1116}(533, \cdot)\) 1116.2.p.a 64 2
1116.2.v \(\chi_{1116}(247, \cdot)\) n/a 376 2
1116.2.w \(\chi_{1116}(595, \cdot)\) n/a 156 2
1116.2.z \(\chi_{1116}(367, \cdot)\) n/a 376 2
1116.2.bb \(\chi_{1116}(161, \cdot)\) 1116.2.bb.a 4 2
1116.2.bb.b 16
1116.2.bc \(\chi_{1116}(185, \cdot)\) 1116.2.bc.a 64 2
1116.2.bf \(\chi_{1116}(677, \cdot)\) 1116.2.bf.a 64 2
1116.2.bh \(\chi_{1116}(311, \cdot)\) n/a 360 2
1116.2.bi \(\chi_{1116}(935, \cdot)\) n/a 128 2
1116.2.bl \(\chi_{1116}(191, \cdot)\) n/a 376 2
1116.2.bm \(\chi_{1116}(223, \cdot)\) n/a 376 2
1116.2.bp \(\chi_{1116}(89, \cdot)\) 1116.2.bp.a 48 4
1116.2.br \(\chi_{1116}(35, \cdot)\) n/a 256 4
1116.2.bu \(\chi_{1116}(91, \cdot)\) n/a 312 4
1116.2.bw \(\chi_{1116}(121, \cdot)\) n/a 256 8
1116.2.bx \(\chi_{1116}(97, \cdot)\) n/a 256 8
1116.2.by \(\chi_{1116}(289, \cdot)\) n/a 104 8
1116.2.bz \(\chi_{1116}(49, \cdot)\) n/a 256 8
1116.2.cb \(\chi_{1116}(65, \cdot)\) n/a 256 8
1116.2.cd \(\chi_{1116}(479, \cdot)\) n/a 1504 8
1116.2.ce \(\chi_{1116}(115, \cdot)\) n/a 1504 8
1116.2.ch \(\chi_{1116}(55, \cdot)\) n/a 624 8
1116.2.ci \(\chi_{1116}(139, \cdot)\) n/a 1504 8
1116.2.cn \(\chi_{1116}(59, \cdot)\) n/a 1504 8
1116.2.cq \(\chi_{1116}(71, \cdot)\) n/a 512 8
1116.2.cr \(\chi_{1116}(47, \cdot)\) n/a 1504 8
1116.2.ct \(\chi_{1116}(137, \cdot)\) n/a 256 8
1116.2.cw \(\chi_{1116}(29, \cdot)\) n/a 256 8
1116.2.cx \(\chi_{1116}(17, \cdot)\) 1116.2.cx.a 80 8
1116.2.db \(\chi_{1116}(43, \cdot)\) n/a 1504 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1116))\)\(^{\oplus 1}\)