# Properties

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

## 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

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