## Defining parameters

 Level: $$N$$ = $$128 = 2^{7}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$1024$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(128))$$.

Total New Old
Modular forms 81 25 56
Cusp forms 1 1 0
Eisenstein series 80 24 56

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{9} + O(q^{10})$$ $$q - q^{9} - 2q^{17} + q^{25} + 2q^{41} + q^{49} - 2q^{73} + q^{81} - 2q^{89} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$

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
128.1.c $$\chi_{128}(127, \cdot)$$ None 0 1
128.1.d $$\chi_{128}(63, \cdot)$$ 128.1.d.a 1 1
128.1.f $$\chi_{128}(31, \cdot)$$ None 0 2
128.1.h $$\chi_{128}(15, \cdot)$$ None 0 4
128.1.j $$\chi_{128}(7, \cdot)$$ None 0 8
128.1.l $$\chi_{128}(3, \cdot)$$ None 0 16