## Defining parameters

 Level: $$N$$ = $$8 = 2^{3}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(8))$$.

Total New Old
Modular forms 7 3 4
Cusp forms 1 1 0
Eisenstein series 6 2 4

## Trace form

 $$q - 2 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{8} - 5 q^{9} + O(q^{10})$$ $$q - 2 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{8} - 5 q^{9} + 14 q^{11} - 8 q^{12} + 16 q^{16} + 2 q^{17} + 10 q^{18} - 34 q^{19} - 28 q^{22} + 16 q^{24} + 25 q^{25} + 28 q^{27} - 32 q^{32} - 28 q^{33} - 4 q^{34} - 20 q^{36} + 68 q^{38} - 46 q^{41} + 14 q^{43} + 56 q^{44} - 32 q^{48} + 49 q^{49} - 50 q^{50} - 4 q^{51} - 56 q^{54} + 68 q^{57} - 82 q^{59} + 64 q^{64} + 56 q^{66} + 62 q^{67} + 8 q^{68} + 40 q^{72} - 142 q^{73} - 50 q^{75} - 136 q^{76} - 11 q^{81} + 92 q^{82} + 158 q^{83} - 28 q^{86} - 112 q^{88} + 146 q^{89} + 64 q^{96} - 94 q^{97} - 98 q^{98} - 70 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$

We only show spaces with odd 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
8.3.c $$\chi_{8}(7, \cdot)$$ None 0 1
8.3.d $$\chi_{8}(3, \cdot)$$ 8.3.d.a 1 1