# Properties

 Label 2352.1.d Level $2352$ Weight $1$ Character orbit 2352.d Rep. character $\chi_{2352}(785,\cdot)$ Character field $\Q$ Dimension $2$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ 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 56 7 49
Cusp forms 8 2 6
Eisenstein series 48 5 43

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q + 2q^{9} + O(q^{10})$$ $$2q + 2q^{9} + 2q^{25} - 2q^{37} + 2q^{39} + 2q^{43} - 2q^{57} + 2q^{67} + 2q^{79} + 2q^{81} - 2q^{93} + O(q^{100})$$

## 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.d.a $$1$$ $$1.174$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{9}-q^{13}+q^{19}+q^{25}-q^{27}+\cdots$$
2352.1.d.b $$1$$ $$1.174$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}+q^{13}-q^{19}+q^{25}+q^{27}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2352, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2352, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 3}$$