# Properties

 Label 2520.1.hf Level $2520$ Weight $1$ Character orbit 2520.hf Rep. character $\chi_{2520}(293,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $32$ Newform subspaces $2$ Sturm bound $576$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2520.hf (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2520$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2520, [\chi])$$.

Total New Old
Modular forms 64 64 0
Cusp forms 32 32 0
Eisenstein series 32 32 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 32 0 0 0

## Trace form

 $$32q + O(q^{10})$$ $$32q + 16q^{16} - 8q^{18} - 24q^{23} - 8q^{57} + 8q^{60} + 8q^{63} - 24q^{65} - 16q^{72} - 16q^{78} - 24q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2520, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2520.1.hf.a $$16$$ $$1.258$$ $$\Q(\zeta_{48})$$ $$D_{24}$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{48}^{2}q^{2}+\zeta_{48}^{15}q^{3}+\zeta_{48}^{4}q^{4}+\cdots$$
2520.1.hf.b $$16$$ $$1.258$$ $$\Q(\zeta_{48})$$ $$D_{24}$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{48}^{14}q^{2}+\zeta_{48}^{15}q^{3}-\zeta_{48}^{4}q^{4}+\cdots$$