# Properties

 Label 256.1 Level 256 Weight 1 Dimension 1 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 4096 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$256 = 2^{8}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$4096$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(256))$$.

Total New Old
Modular forms 179 53 126
Cusp forms 3 1 2
Eisenstein series 176 52 124

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 $$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$

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
256.1.c $$\chi_{256}(255, \cdot)$$ 256.1.c.a 1 1
256.1.d $$\chi_{256}(127, \cdot)$$ None 0 1
256.1.f $$\chi_{256}(63, \cdot)$$ None 0 2
256.1.h $$\chi_{256}(31, \cdot)$$ None 0 4
256.1.j $$\chi_{256}(15, \cdot)$$ None 0 8
256.1.l $$\chi_{256}(7, \cdot)$$ None 0 16
256.1.n $$\chi_{256}(3, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(256))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(256)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 2}$$