# Properties

 Label 2520.1.eq Level $2520$ Weight $1$ Character orbit 2520.eq Rep. character $\chi_{2520}(899,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $2$ Sturm bound $576$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2520.eq (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$840$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$5$$

## Dimensions

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

Total New Old
Modular forms 48 16 32
Cusp forms 16 16 0
Eisenstein series 32 0 32

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16q + 8q^{4} + O(q^{10})$$ $$16q + 8q^{4} - 8q^{16} - 8q^{25} - 16q^{64} - 8q^{91} - 24q^{94} + O(q^{100})$$

## 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.eq.a $$8$$ $$1.258$$ $$\Q(\zeta_{24})$$ $$D_{12}$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{4}q^{5}+\cdots$$
2520.1.eq.b $$8$$ $$1.258$$ $$\Q(\zeta_{24})$$ $$D_{12}$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+\zeta_{24}^{4}q^{5}+\cdots$$