Properties

Label 660.2
Level 660
Weight 2
Dimension 4432
Nonzero newspaces 24
Newform subspaces 47
Sturm bound 46080
Trace bound 9

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Defining parameters

Level: \( N \) = \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 47 \)
Sturm bound: \(46080\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(660))\).

Total New Old
Modular forms 12320 4656 7664
Cusp forms 10721 4432 6289
Eisenstein series 1599 224 1375

Trace form

\( 4432 q - 4 q^{3} - 4 q^{4} - 4 q^{5} - 14 q^{6} - 12 q^{7} + 24 q^{8} - 20 q^{9} + O(q^{10}) \) \( 4432 q - 4 q^{3} - 4 q^{4} - 4 q^{5} - 14 q^{6} - 12 q^{7} + 24 q^{8} - 20 q^{9} + 20 q^{10} - 12 q^{11} - 12 q^{12} - 12 q^{13} + 20 q^{14} + 28 q^{15} + 20 q^{16} + 60 q^{17} - 22 q^{18} + 60 q^{19} + 10 q^{20} + 24 q^{21} + 92 q^{22} + 40 q^{23} + 2 q^{24} + 8 q^{25} + 68 q^{26} + 2 q^{27} + 32 q^{28} + 16 q^{29} - 82 q^{30} - 8 q^{31} - 40 q^{32} + 48 q^{33} - 168 q^{34} - 12 q^{35} - 110 q^{36} + 120 q^{37} - 132 q^{38} + 70 q^{39} - 132 q^{40} + 128 q^{41} - 156 q^{42} + 104 q^{43} - 140 q^{44} + 19 q^{45} - 112 q^{46} + 100 q^{47} - 80 q^{48} + 216 q^{49} - 38 q^{50} + 94 q^{51} - 40 q^{52} + 212 q^{53} - 68 q^{54} + 148 q^{55} + 48 q^{56} - 70 q^{57} + 72 q^{58} + 76 q^{59} + 18 q^{60} + 12 q^{61} + 112 q^{62} - 106 q^{63} + 92 q^{64} + 20 q^{65} - 96 q^{66} + 28 q^{67} + 32 q^{68} - 134 q^{69} - 84 q^{70} - 80 q^{71} - 204 q^{72} - 236 q^{73} - 100 q^{74} - 54 q^{75} - 264 q^{76} - 148 q^{77} - 272 q^{78} - 108 q^{79} - 118 q^{80} - 212 q^{81} - 332 q^{82} - 60 q^{83} - 352 q^{84} - 222 q^{85} - 288 q^{86} - 40 q^{87} - 444 q^{88} - 120 q^{89} - 300 q^{90} - 28 q^{91} - 372 q^{92} - 148 q^{93} - 608 q^{94} - 130 q^{95} - 368 q^{96} - 96 q^{97} - 488 q^{98} - 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
660.2.a \(\chi_{660}(1, \cdot)\) 660.2.a.a 1 1
660.2.a.b 1
660.2.a.c 1
660.2.a.d 1
660.2.a.e 2
660.2.a.f 2
660.2.c \(\chi_{660}(529, \cdot)\) 660.2.c.a 2 1
660.2.c.b 2
660.2.c.c 4
660.2.d \(\chi_{660}(461, \cdot)\) 660.2.d.a 16 1
660.2.f \(\chi_{660}(551, \cdot)\) 660.2.f.a 40 1
660.2.f.b 40
660.2.i \(\chi_{660}(439, \cdot)\) 660.2.i.a 36 1
660.2.i.b 36
660.2.k \(\chi_{660}(571, \cdot)\) 660.2.k.a 4 1
660.2.k.b 4
660.2.k.c 20
660.2.k.d 20
660.2.l \(\chi_{660}(419, \cdot)\) 660.2.l.a 60 1
660.2.l.b 60
660.2.n \(\chi_{660}(329, \cdot)\) 660.2.n.a 4 1
660.2.n.b 4
660.2.n.c 16
660.2.q \(\chi_{660}(263, \cdot)\) 660.2.q.a 272 2
660.2.t \(\chi_{660}(353, \cdot)\) 660.2.t.a 20 2
660.2.t.b 20
660.2.u \(\chi_{660}(67, \cdot)\) 660.2.u.a 60 2
660.2.u.b 60
660.2.x \(\chi_{660}(373, \cdot)\) 660.2.x.a 24 2
660.2.y \(\chi_{660}(181, \cdot)\) 660.2.y.a 8 4
660.2.y.b 8
660.2.y.c 8
660.2.y.d 8
660.2.bb \(\chi_{660}(29, \cdot)\) 660.2.bb.a 96 4
660.2.bd \(\chi_{660}(59, \cdot)\) 660.2.bd.a 544 4
660.2.be \(\chi_{660}(151, \cdot)\) 660.2.be.a 96 4
660.2.be.b 96
660.2.bg \(\chi_{660}(19, \cdot)\) 660.2.bg.a 144 4
660.2.bg.b 144
660.2.bj \(\chi_{660}(71, \cdot)\) 660.2.bj.a 384 4
660.2.bl \(\chi_{660}(41, \cdot)\) 660.2.bl.a 16 4
660.2.bl.b 48
660.2.bm \(\chi_{660}(49, \cdot)\) 660.2.bm.a 48 4
660.2.bo \(\chi_{660}(13, \cdot)\) 660.2.bo.a 96 8
660.2.br \(\chi_{660}(103, \cdot)\) 660.2.br.a 576 8
660.2.bs \(\chi_{660}(53, \cdot)\) 660.2.bs.a 192 8
660.2.bv \(\chi_{660}(83, \cdot)\) 660.2.bv.a 1088 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(660))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(660)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)