# Properties

 Label 2548.1.q Level $2548$ Weight $1$ Character orbit 2548.q Rep. character $\chi_{2548}(263,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $3$ Sturm bound $392$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2548 = 2^{2} \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2548.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$364$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$392$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2548, [\chi])$$.

Total New Old
Modular forms 40 24 16
Cusp forms 8 8 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 8 0 0 0

## Trace form

 $$8 q - 4 q^{4} + 8 q^{9} + O(q^{10})$$ $$8 q - 4 q^{4} + 8 q^{9} - 4 q^{16} - 4 q^{25} - 4 q^{36} + 4 q^{50} + 4 q^{53} - 8 q^{58} + 8 q^{64} - 4 q^{65} + 4 q^{74} + 8 q^{81} - 8 q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2548, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2548.1.q.a $2$ $1.272$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots$$
2548.1.q.b $2$ $1.272$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots$$
2548.1.q.c $4$ $1.272$ $$\Q(\zeta_{12})$$ $D_{6}$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$$