# Properties

 Label 66.2 Level 66 Weight 2 Dimension 31 Nonzero newspaces 4 Newform subspaces 9 Sturm bound 480 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$66 = 2 \cdot 3 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$9$$ Sturm bound: $$480$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(66))$$.

Total New Old
Modular forms 160 31 129
Cusp forms 81 31 50
Eisenstein series 79 0 79

## Trace form

 $$31 q + q^{2} + q^{3} + q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 19 q^{9} + O(q^{10})$$ $$31 q + q^{2} + q^{3} + q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 19 q^{9} - 14 q^{10} - 9 q^{11} - 9 q^{12} - 6 q^{13} - 12 q^{14} - 24 q^{15} + q^{16} - 22 q^{17} - 4 q^{18} - 10 q^{19} + 6 q^{20} - 12 q^{21} + 11 q^{22} + 4 q^{23} + 6 q^{24} - 9 q^{25} + 14 q^{26} + 31 q^{27} + 8 q^{28} + 10 q^{29} + 36 q^{30} + 12 q^{31} + q^{32} + 56 q^{33} + 18 q^{34} + 28 q^{35} + 6 q^{36} + 38 q^{37} + 20 q^{38} + 24 q^{39} + 6 q^{40} + 22 q^{41} + 18 q^{42} - 16 q^{43} - 9 q^{44} + 6 q^{45} - 16 q^{46} - 32 q^{47} + q^{48} - 63 q^{49} - 9 q^{50} - 37 q^{51} - 26 q^{52} - 6 q^{53} - 9 q^{54} - 34 q^{55} + 8 q^{56} + 15 q^{57} - 50 q^{58} - 14 q^{60} - 38 q^{61} - 28 q^{62} - 2 q^{63} + q^{64} - 36 q^{65} - 49 q^{66} - 32 q^{67} - 22 q^{68} - 6 q^{69} - 32 q^{70} - 8 q^{71} - 19 q^{72} - 6 q^{73} - 2 q^{74} - 14 q^{75} + 8 q^{77} - 26 q^{78} + 20 q^{79} - 14 q^{80} - 39 q^{81} + 32 q^{82} + 24 q^{83} + 8 q^{84} + 48 q^{85} - 16 q^{86} + 30 q^{87} - 9 q^{88} + 30 q^{89} + 16 q^{90} + 152 q^{91} + 24 q^{92} + 2 q^{93} + 88 q^{94} + 60 q^{95} + q^{96} + 68 q^{97} + 57 q^{98} + 41 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$

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
66.2.a $$\chi_{66}(1, \cdot)$$ 66.2.a.a 1 1
66.2.a.b 1
66.2.a.c 1
66.2.b $$\chi_{66}(65, \cdot)$$ 66.2.b.a 2 1
66.2.b.b 2
66.2.e $$\chi_{66}(25, \cdot)$$ 66.2.e.a 4 4
66.2.e.b 4
66.2.h $$\chi_{66}(17, \cdot)$$ 66.2.h.a 8 4
66.2.h.b 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(66))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(66)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 2}$$