# Properties

 Label 128.1.d Level $128$ Weight $1$ Character orbit 128.d Rep. character $\chi_{128}(63,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 128.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(128, [\chi])$$.

Total New Old
Modular forms 9 1 8
Cusp forms 1 1 0
Eisenstein series 8 0 8

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 $$S_{1}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
128.1.d.a $$1$$ $$0.064$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots$$