# Properties

 Label 676.1.i Level $676$ Weight $1$ Character orbit 676.i Rep. character $\chi_{676}(23,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $91$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$676 = 2^{2} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 676.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$52$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$91$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(676, [\chi])$$.

Total New Old
Modular forms 32 24 8
Cusp forms 4 4 0
Eisenstein series 28 20 8

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

 $$4 q + 2 q^{4} - 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{4} - 2 q^{9} - 2 q^{10} - 2 q^{16} - 2 q^{17} + 2 q^{29} + 2 q^{36} - 4 q^{40} + 2 q^{49} - 4 q^{53} + 2 q^{61} - 4 q^{64} + 2 q^{68} + 2 q^{74} - 2 q^{81} - 2 q^{82} + 4 q^{90} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(676, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
676.1.i.a $$4$$ $$0.337$$ $$\Q(\zeta_{12})$$ $$D_{3}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$