# Properties

 Label 260.2.d Level $260$ Weight $2$ Character orbit 260.d Rep. character $\chi_{260}(129,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $84$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 260.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$84$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(260, [\chi])$$.

Total New Old
Modular forms 48 8 40
Cusp forms 36 8 28
Eisenstein series 12 0 12

## Trace form

 $$8 q - 16 q^{9} + O(q^{10})$$ $$8 q - 16 q^{9} + 8 q^{25} - 24 q^{29} + 24 q^{35} + 24 q^{39} + 24 q^{49} - 32 q^{51} - 8 q^{55} - 8 q^{61} - 8 q^{69} - 48 q^{75} + 16 q^{79} + 80 q^{81} - 56 q^{91} + 24 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(260, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
260.2.d.a $8$ $2.076$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}-\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(260, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(260, [\chi]) \cong$$