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Properties

Label 1332.2
Level 1332
Weight 2
Dimension 22393
Nonzero newspaces 48
Sturm bound 196992
Trace bound 22

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Defining parameters

Level: \( N \) = \( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(196992\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1332))\).

Total New Old
Modular forms 50688 23025 27663
Cusp forms 47809 22393 25416
Eisenstein series 2879 632 2247

Trace form

\( 22393 q - 48 q^{2} - 44 q^{4} - 90 q^{5} - 66 q^{6} + 6 q^{7} - 54 q^{8} - 120 q^{9} + O(q^{10}) \) \( 22393 q - 48 q^{2} - 44 q^{4} - 90 q^{5} - 66 q^{6} + 6 q^{7} - 54 q^{8} - 120 q^{9} - 154 q^{10} + 6 q^{11} - 84 q^{12} - 94 q^{13} - 78 q^{14} - 18 q^{15} - 68 q^{16} - 132 q^{17} - 108 q^{18} - 90 q^{20} - 138 q^{21} - 60 q^{22} - 6 q^{23} - 78 q^{24} - 90 q^{25} - 54 q^{26} - 138 q^{28} - 132 q^{29} - 36 q^{30} - 36 q^{31} + 12 q^{32} - 174 q^{33} - 28 q^{34} - 42 q^{35} - 6 q^{36} - 356 q^{37} - 54 q^{38} + 6 q^{39} - 58 q^{40} - 204 q^{41} - 36 q^{42} - 54 q^{43} - 54 q^{44} - 174 q^{45} - 186 q^{46} - 36 q^{47} - 114 q^{48} - 170 q^{49} - 96 q^{50} - 118 q^{52} - 84 q^{53} - 150 q^{54} - 36 q^{55} - 90 q^{56} - 156 q^{57} - 100 q^{58} + 30 q^{59} - 84 q^{60} - 73 q^{61} + 36 q^{62} + 6 q^{63} - 56 q^{64} + 27 q^{65} - 24 q^{66} + 54 q^{67} + 84 q^{68} - 66 q^{69} + 156 q^{70} + 120 q^{71} - 30 q^{72} - 100 q^{73} + 120 q^{74} + 24 q^{75} + 96 q^{76} + 18 q^{77} - 48 q^{78} + 102 q^{79} + 144 q^{80} - 120 q^{81} - 82 q^{82} + 18 q^{83} - 132 q^{84} - 47 q^{85} + 30 q^{86} + 18 q^{87} + 78 q^{88} - 87 q^{89} - 84 q^{90} + 66 q^{91} - 84 q^{92} - 126 q^{93} - 18 q^{94} + 192 q^{95} - 96 q^{96} + 62 q^{97} - 54 q^{98} + 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)

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
1332.2.a \(\chi_{1332}(1, \cdot)\) 1332.2.a.a 1 1
1332.2.a.b 1
1332.2.a.c 1
1332.2.a.d 1
1332.2.a.e 1
1332.2.a.f 2
1332.2.a.g 2
1332.2.a.h 2
1332.2.a.i 4
1332.2.c \(\chi_{1332}(1259, \cdot)\) 1332.2.c.a 36 1
1332.2.c.b 36
1332.2.e \(\chi_{1332}(73, \cdot)\) 1332.2.e.a 2 1
1332.2.e.b 2
1332.2.e.c 4
1332.2.e.d 4
1332.2.e.e 4
1332.2.g \(\chi_{1332}(1331, \cdot)\) 1332.2.g.a 4 1
1332.2.g.b 4
1332.2.g.c 4
1332.2.g.d 64
1332.2.i \(\chi_{1332}(445, \cdot)\) 1332.2.i.a 2 2
1332.2.i.b 2
1332.2.i.c 34
1332.2.i.d 34
1332.2.j \(\chi_{1332}(433, \cdot)\) 1332.2.j.a 2 2
1332.2.j.b 2
1332.2.j.c 2
1332.2.j.d 4
1332.2.j.e 6
1332.2.j.f 6
1332.2.j.g 12
1332.2.k \(\chi_{1332}(565, \cdot)\) 1332.2.k.a 2 2
1332.2.k.b 74
1332.2.l \(\chi_{1332}(121, \cdot)\) 1332.2.l.a 2 2
1332.2.l.b 74
1332.2.n \(\chi_{1332}(487, \cdot)\) n/a 186 2
1332.2.p \(\chi_{1332}(413, \cdot)\) 1332.2.p.a 28 2
1332.2.q \(\chi_{1332}(529, \cdot)\) 1332.2.q.a 76 2
1332.2.s \(\chi_{1332}(491, \cdot)\) n/a 448 2
1332.2.u \(\chi_{1332}(455, \cdot)\) n/a 448 2
1332.2.z \(\chi_{1332}(443, \cdot)\) n/a 448 2
1332.2.bb \(\chi_{1332}(323, \cdot)\) n/a 152 2
1332.2.bd \(\chi_{1332}(47, \cdot)\) n/a 448 2
1332.2.bg \(\chi_{1332}(517, \cdot)\) 1332.2.bg.a 4 2
1332.2.bg.b 72
1332.2.bi \(\chi_{1332}(397, \cdot)\) 1332.2.bi.a 2 2
1332.2.bi.b 2
1332.2.bi.c 2
1332.2.bi.d 2
1332.2.bi.e 2
1332.2.bi.f 2
1332.2.bi.g 4
1332.2.bi.h 8
1332.2.bi.i 8
1332.2.bk \(\chi_{1332}(371, \cdot)\) n/a 432 2
1332.2.bm \(\chi_{1332}(359, \cdot)\) n/a 152 2
1332.2.bn \(\chi_{1332}(85, \cdot)\) 1332.2.bn.a 76 2
1332.2.bq \(\chi_{1332}(11, \cdot)\) n/a 448 2
1332.2.bs \(\chi_{1332}(49, \cdot)\) n/a 228 6
1332.2.bt \(\chi_{1332}(145, \cdot)\) 1332.2.bt.a 6 6
1332.2.bt.b 12
1332.2.bt.c 18
1332.2.bt.d 24
1332.2.bt.e 36
1332.2.bu \(\chi_{1332}(229, \cdot)\) n/a 228 6
1332.2.bv \(\chi_{1332}(103, \cdot)\) n/a 896 4
1332.2.by \(\chi_{1332}(29, \cdot)\) n/a 152 4
1332.2.bz \(\chi_{1332}(401, \cdot)\) n/a 152 4
1332.2.cc \(\chi_{1332}(125, \cdot)\) 1332.2.cc.a 56 4
1332.2.ce \(\chi_{1332}(319, \cdot)\) n/a 896 4
1332.2.cf \(\chi_{1332}(31, \cdot)\) n/a 896 4
1332.2.ci \(\chi_{1332}(199, \cdot)\) n/a 372 4
1332.2.cj \(\chi_{1332}(245, \cdot)\) n/a 152 4
1332.2.cp \(\chi_{1332}(71, \cdot)\) n/a 456 6
1332.2.cq \(\chi_{1332}(155, \cdot)\) n/a 1344 6
1332.2.cr \(\chi_{1332}(95, \cdot)\) n/a 1344 6
1332.2.cs \(\chi_{1332}(215, \cdot)\) n/a 456 6
1332.2.ct \(\chi_{1332}(289, \cdot)\) 1332.2.ct.a 6 6
1332.2.ct.b 6
1332.2.ct.c 12
1332.2.ct.d 18
1332.2.ct.e 24
1332.2.ct.f 24
1332.2.cu \(\chi_{1332}(781, \cdot)\) n/a 228 6
1332.2.dd \(\chi_{1332}(25, \cdot)\) n/a 228 6
1332.2.de \(\chi_{1332}(707, \cdot)\) n/a 1344 6
1332.2.df \(\chi_{1332}(83, \cdot)\) n/a 1344 6
1332.2.di \(\chi_{1332}(79, \cdot)\) n/a 2688 12
1332.2.dj \(\chi_{1332}(113, \cdot)\) n/a 456 12
1332.2.dk \(\chi_{1332}(17, \cdot)\) n/a 144 12
1332.2.dl \(\chi_{1332}(19, \cdot)\) n/a 1116 12
1332.2.dq \(\chi_{1332}(5, \cdot)\) n/a 456 12
1332.2.dr \(\chi_{1332}(187, \cdot)\) n/a 2688 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 1}\)