# Properties

 Label 666.2 Level 666 Weight 2 Dimension 3245 Nonzero newspaces 24 Newform subspaces 83 Sturm bound 49248 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$83$$ Sturm bound: $$49248$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(666))$$.

Total New Old
Modular forms 12888 3245 9643
Cusp forms 11737 3245 8492
Eisenstein series 1151 0 1151

## Trace form

 $$3245 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10})$$ $$3245 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} + q^{26} + 4 q^{28} + 48 q^{29} + 100 q^{31} + 2 q^{32} + 18 q^{33} + 66 q^{34} + 108 q^{35} - 6 q^{36} + 92 q^{37} + 34 q^{38} + 45 q^{40} + 126 q^{41} + 70 q^{43} + 12 q^{44} + 96 q^{46} + 24 q^{47} - 6 q^{48} + 42 q^{49} - q^{50} - 18 q^{51} + 4 q^{52} - 48 q^{53} - 18 q^{54} + 4 q^{56} - 6 q^{57} + 12 q^{58} + 42 q^{59} + 61 q^{61} + 16 q^{62} + 24 q^{63} - 4 q^{64} + 81 q^{65} + 46 q^{67} - 6 q^{68} + 120 q^{71} - 6 q^{72} + 28 q^{73} - 4 q^{74} + 30 q^{75} - 2 q^{76} + 60 q^{77} + 12 q^{78} + 64 q^{79} + 18 q^{81} - 36 q^{82} + 60 q^{83} + 12 q^{84} + 81 q^{85} - 2 q^{86} - 36 q^{87} - 6 q^{88} + 21 q^{89} - 16 q^{91} - 120 q^{92} - 216 q^{93} - 228 q^{94} - 432 q^{95} - 422 q^{97} - 420 q^{98} - 396 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(666))$$

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
666.2.a $$\chi_{666}(1, \cdot)$$ 666.2.a.a 1 1
666.2.a.b 1
666.2.a.c 1
666.2.a.d 1
666.2.a.e 1
666.2.a.f 1
666.2.a.g 1
666.2.a.h 2
666.2.a.i 2
666.2.a.j 2
666.2.a.k 2
666.2.c $$\chi_{666}(73, \cdot)$$ 666.2.c.a 2 1
666.2.c.b 4
666.2.c.c 4
666.2.c.d 4
666.2.e $$\chi_{666}(223, \cdot)$$ 666.2.e.a 2 2
666.2.e.b 2
666.2.e.c 12
666.2.e.d 14
666.2.e.e 20
666.2.e.f 22
666.2.f $$\chi_{666}(343, \cdot)$$ 666.2.f.a 2 2
666.2.f.b 2
666.2.f.c 2
666.2.f.d 2
666.2.f.e 2
666.2.f.f 2
666.2.f.g 4
666.2.f.h 4
666.2.f.i 4
666.2.f.j 6
666.2.g $$\chi_{666}(211, \cdot)$$ 666.2.g.a 2 2
666.2.g.b 36
666.2.g.c 38
666.2.h $$\chi_{666}(121, \cdot)$$ 666.2.h.a 2 2
666.2.h.b 36
666.2.h.c 38
666.2.j $$\chi_{666}(179, \cdot)$$ 666.2.j.a 4 2
666.2.j.b 4
666.2.j.c 4
666.2.j.d 8
666.2.k $$\chi_{666}(175, \cdot)$$ 666.2.k.a 76 2
666.2.q $$\chi_{666}(295, \cdot)$$ 666.2.q.a 4 2
666.2.q.b 72
666.2.s $$\chi_{666}(307, \cdot)$$ 666.2.s.a 4 2
666.2.s.b 4
666.2.s.c 4
666.2.s.d 4
666.2.s.e 4
666.2.s.f 8
666.2.t $$\chi_{666}(85, \cdot)$$ 666.2.t.a 76 2
666.2.w $$\chi_{666}(7, \cdot)$$ 666.2.w.a 114 6
666.2.w.b 114
666.2.x $$\chi_{666}(127, \cdot)$$ 666.2.x.a 6 6
666.2.x.b 6
666.2.x.c 6
666.2.x.d 6
666.2.x.e 6
666.2.x.f 12
666.2.x.g 12
666.2.x.h 24
666.2.x.i 24
666.2.y $$\chi_{666}(229, \cdot)$$ 666.2.y.a 114 6
666.2.y.b 114
666.2.ba $$\chi_{666}(23, \cdot)$$ 666.2.ba.a 152 4
666.2.bb $$\chi_{666}(191, \cdot)$$ 666.2.bb.a 152 4
666.2.be $$\chi_{666}(125, \cdot)$$ 666.2.be.a 8 4
666.2.be.b 8
666.2.be.c 8
666.2.be.d 16
666.2.bf $$\chi_{666}(245, \cdot)$$ 666.2.bf.a 152 4
666.2.bj $$\chi_{666}(289, \cdot)$$ 666.2.bj.a 12 6
666.2.bj.b 12
666.2.bj.c 12
666.2.bj.d 12
666.2.bj.e 24
666.2.bj.f 24
666.2.bk $$\chi_{666}(115, \cdot)$$ 666.2.bk.a 228 6
666.2.bp $$\chi_{666}(25, \cdot)$$ 666.2.bp.a 228 6
666.2.br $$\chi_{666}(59, \cdot)$$ 666.2.br.a 456 12
666.2.bs $$\chi_{666}(17, \cdot)$$ 666.2.bs.a 72 12
666.2.bs.b 96
666.2.bv $$\chi_{666}(5, \cdot)$$ 666.2.bv.a 456 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(666))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(666)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(111))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(222))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(333))$$$$^{\oplus 2}$$