# Properties

 Label 720.1.r Level $720$ Weight $1$ Character orbit 720.r Rep. character $\chi_{720}(19,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $1$ Sturm bound $144$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 720.r (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(720, [\chi])$$.

Total New Old
Modular forms 20 8 12
Cusp forms 4 4 0
Eisenstein series 16 4 12

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q + O(q^{10})$$ $$4q - 4q^{10} - 4q^{16} + 4q^{19} - 4q^{34} + 4q^{46} + 4q^{49} - 4q^{61} - 4q^{76} - 4q^{85} + 4q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(720, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
720.1.r.a $$4$$ $$0.359$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$$