# Properties

 Label 2352.1.by Level $2352$ Weight $1$ Character orbit 2352.by Rep. character $\chi_{2352}(335,\cdot)$ Character field $\Q(\zeta_{14})$ Dimension $12$ Newform subspaces $2$ Sturm bound $448$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2352.by (of order $$14$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$588$$ Character field: $$\Q(\zeta_{14})$$ Newform subspaces: $$2$$ Sturm bound: $$448$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2352, [\chi])$$.

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12q - 2q^{9} + O(q^{10})$$ $$12q - 2q^{9} + 2q^{21} + 2q^{25} - 10q^{37} - 2q^{49} + 4q^{57} - 14q^{61} - 2q^{81} - 4q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2352, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2352.1.by.a $$6$$ $$1.174$$ $$\Q(\zeta_{14})$$ $$D_{14}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $$q-\zeta_{14}q^{3}+\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$$
2352.1.by.b $$6$$ $$1.174$$ $$\Q(\zeta_{14})$$ $$D_{14}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+\zeta_{14}q^{3}-\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$$