# Properties

 Label 3200.1.bz Level $3200$ Weight $1$ Character orbit 3200.bz Rep. character $\chi_{3200}(577,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $16$ Newform subspaces $2$ Sturm bound $480$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3200.bz (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$200$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ Sturm bound: $$480$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3200, [\chi])$$.

Total New Old
Modular forms 144 16 128
Cusp forms 16 16 0
Eisenstein series 128 0 128

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

 $$16 q + O(q^{10})$$ $$16 q - 4 q^{17} + 4 q^{25} + 4 q^{65} + 4 q^{73} + 4 q^{81} + 20 q^{89} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3200, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3200.1.bz.a $8$ $1.597$ $$\Q(\zeta_{20})$$ $D_{20}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(\zeta_{20}^{3}-\zeta_{20}^{6}+\cdots)q^{13}+\cdots$$
3200.1.bz.b $8$ $1.597$ $$\Q(\zeta_{20})$$ $D_{20}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(-\zeta_{20}^{3}+\zeta_{20}^{6}+\cdots)q^{13}+\cdots$$