# Properties

 Label 768.1.e Level $768$ Weight $1$ Character orbit 768.e Rep. character $\chi_{768}(257,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $128$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 768.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$128$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(768, [\chi])$$.

Total New Old
Modular forms 28 8 20
Cusp forms 4 4 0
Eisenstein series 24 4 20

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q + O(q^{10})$$ $$4 q + 4 q^{25} - 4 q^{33} - 4 q^{49} - 4 q^{57} + 4 q^{81} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(768, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
768.1.e.a $1$ $0.383$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots$$
768.1.e.b $1$ $0.383$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots$$
768.1.e.c $2$ $0.383$ $$\Q(\sqrt{-1})$$ $D_{2}$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots$$