# Properties

 Label 980.1.n Level $980$ Weight $1$ Character orbit 980.n Rep. character $\chi_{980}(129,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $168$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 980.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$168$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(980, [\chi])$$.

Total New Old
Modular forms 52 4 48
Cusp forms 4 4 0
Eisenstein series 48 0 48

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

 $$4 q + O(q^{10})$$ $$4 q + 2 q^{11} - 4 q^{15} - 2 q^{25} - 4 q^{29} - 2 q^{39} - 2 q^{51} + 2 q^{65} + 8 q^{71} + 2 q^{79} + 2 q^{81} - 4 q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(980, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.1.n.a $2$ $0.489$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-35})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots$$
980.1.n.b $2$ $0.489$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-35})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots$$