## Defining parameters

 Level: $$N$$ = $$668 = 2^{2} \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$55776$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(668))$$.

Total New Old
Modular forms 14359 8300 6059
Cusp forms 13530 7968 5562
Eisenstein series 829 332 497

## Trace form

 $$7968q - 83q^{2} - 83q^{4} - 166q^{5} - 83q^{6} - 83q^{8} - 166q^{9} + O(q^{10})$$ $$7968q - 83q^{2} - 83q^{4} - 166q^{5} - 83q^{6} - 83q^{8} - 166q^{9} - 83q^{10} - 83q^{12} - 166q^{13} - 83q^{14} - 83q^{16} - 166q^{17} - 83q^{18} - 83q^{20} - 166q^{21} - 83q^{22} - 83q^{24} - 166q^{25} - 83q^{26} - 83q^{28} - 166q^{29} - 83q^{30} - 83q^{32} - 166q^{33} - 83q^{34} - 83q^{36} - 166q^{37} - 83q^{38} - 83q^{40} - 166q^{41} - 83q^{42} - 83q^{44} - 166q^{45} - 83q^{46} - 83q^{48} - 166q^{49} - 83q^{50} - 83q^{52} - 166q^{53} - 83q^{54} - 83q^{56} - 166q^{57} - 83q^{58} - 83q^{60} - 166q^{61} - 83q^{62} - 83q^{64} - 166q^{65} - 83q^{66} - 83q^{68} - 166q^{69} - 83q^{70} - 83q^{72} - 166q^{73} - 83q^{74} - 83q^{76} - 166q^{77} - 83q^{78} - 83q^{80} - 166q^{81} - 83q^{82} - 83q^{84} - 166q^{85} - 83q^{86} - 83q^{88} - 166q^{89} - 83q^{90} - 83q^{92} - 166q^{93} - 83q^{94} - 83q^{96} - 166q^{97} - 83q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(668))$$

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
668.2.a $$\chi_{668}(1, \cdot)$$ 668.2.a.a 2 1
668.2.a.b 5
668.2.a.c 7
668.2.b $$\chi_{668}(667, \cdot)$$ 668.2.b.a 22 1
668.2.b.b 60
668.2.e $$\chi_{668}(9, \cdot)$$ 668.2.e.a 1148 82
668.2.h $$\chi_{668}(15, \cdot)$$ 668.2.h.a 6724 82

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(668))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(668)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 2}$$