# Properties

 Label 1020.1.cl Level $1020$ Weight $1$ Character orbit 1020.cl Rep. character $\chi_{1020}(299,\cdot)$ Character field $\Q(\zeta_{16})$ Dimension $32$ Newform subspaces $2$ Sturm bound $216$ Trace bound $24$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1020.cl (of order $$16$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1020$$ Character field: $$\Q(\zeta_{16})$$ Newform subspaces: $$2$$ Sturm bound: $$216$$ Trace bound: $$24$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1020, [\chi])$$.

Total New Old
Modular forms 96 96 0
Cusp forms 32 32 0
Eisenstein series 64 64 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

 $$32q + O(q^{10})$$ $$32q - 16q^{24} - 16q^{34} - 16q^{36} - 16q^{46} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1020, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1020.1.cl.a $$16$$ $$0.509$$ $$\Q(\zeta_{32})$$ $$D_{16}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{32}^{11}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{6}q^{4}+\cdots$$
1020.1.cl.b $$16$$ $$0.509$$ $$\Q(\zeta_{32})$$ $$D_{16}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{32}^{9}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{2}q^{4}+\cdots$$