## 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

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

## 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