# Properties

 Label 3040.1.cn Level $3040$ Weight $1$ Character orbit 3040.cn Rep. character $\chi_{3040}(189,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $32$ Newform subspaces $1$ Sturm bound $480$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3040 = 2^{5} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3040.cn (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3040$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$1$$ Sturm bound: $$480$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3040, [\chi])$$.

Total New Old
Modular forms 48 48 0
Cusp forms 32 32 0
Eisenstein series 16 16 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

 $$32 q + O(q^{10})$$ $$32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3040, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3040.1.cn.a $32$ $1.517$ $$\Q(\zeta_{64})$$ $D_{32}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{64}^{27}q^{2}+(-\zeta_{64}^{25}-\zeta_{64}^{31}+\cdots)q^{3}+\cdots$$