# Properties

 Label 784.1.y Level $784$ Weight $1$ Character orbit 784.y Rep. character $\chi_{784}(117,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $4$ Newform subspaces $1$ Sturm bound $112$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 784.y (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$112$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$112$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(784, [\chi])$$.

Total New Old
Modular forms 36 20 16
Cusp forms 4 4 0
Eisenstein series 32 16 16

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

 $$4 q + 2 q^{4} + O(q^{10})$$ $$4 q + 2 q^{4} + 2 q^{11} - 2 q^{16} - 2 q^{18} + 4 q^{22} - 4 q^{29} + 2 q^{37} + 4 q^{43} - 2 q^{44} - 4 q^{50} - 2 q^{53} + 2 q^{58} - 4 q^{64} - 2 q^{67} + 2 q^{72} - 2 q^{74} + 2 q^{81} + 2 q^{86} + 2 q^{88} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(784, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
784.1.y.a $4$ $0.391$ $$\Q(\zeta_{12})$$ $D_{4}$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots$$