# Properties

 Label 2520.1.ef Level $2520$ Weight $1$ Character orbit 2520.ef Rep. character $\chi_{2520}(739,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $4$ Sturm bound $576$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2520.ef (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$280$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$576$$ Trace bound: $$2$$

## Dimensions

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

Total New Old
Modular forms 56 20 36
Cusp forms 24 12 12
Eisenstein series 32 8 24

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

 $$12q - 6q^{4} + O(q^{10})$$ $$12q - 6q^{4} + 2q^{10} - 2q^{11} + 2q^{14} - 6q^{16} - 2q^{19} - 6q^{25} - 2q^{26} + 2q^{35} + 2q^{40} + 4q^{41} - 2q^{44} - 2q^{46} - 4q^{49} - 4q^{56} + 4q^{59} + 12q^{64} - 2q^{65} - 2q^{74} + 4q^{76} + 4q^{89} - 4q^{91} + 6q^{94} + O(q^{100})$$

## 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.ef.a $$2$$ $$1.258$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$-2$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{7}+\cdots$$
2520.1.ef.b $$2$$ $$1.258$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$2$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots$$
2520.1.ef.c $$4$$ $$1.258$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-10})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$$
2520.1.ef.d $$4$$ $$1.258$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-10})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2520, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2520, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 3}$$