# Properties

 Label 720.1.j Level $720$ Weight $1$ Character orbit 720.j Rep. character $\chi_{720}(559,\cdot)$ Character field $\Q$ Dimension $1$ 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.j (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ 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 34 1 33
Cusp forms 10 1 9
Eisenstein series 24 0 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q + q^{5} + O(q^{10})$$ $$q + q^{5} + q^{25} - 2 q^{29} + 2 q^{41} - q^{49} - 2 q^{61} - 2 q^{89} + O(q^{100})$$

## 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.j.a $1$ $0.359$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(720, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(720, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 2}$$