# Properties

 Label 520.2.f Level $520$ Weight $2$ Character orbit 520.f Rep. character $\chi_{520}(129,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ Sturm bound $168$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$520 = 2^{3} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 520.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$168$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(520, [\chi])$$.

Total New Old
Modular forms 92 20 72
Cusp forms 76 20 56
Eisenstein series 16 0 16

## Trace form

 $$20 q - 16 q^{9} + O(q^{10})$$ $$20 q - 16 q^{9} - 2 q^{25} + 16 q^{29} - 6 q^{35} - 24 q^{39} + 24 q^{49} - 60 q^{51} + 24 q^{55} - 32 q^{61} - 14 q^{65} - 24 q^{69} + 42 q^{75} + 56 q^{79} + 44 q^{81} + 4 q^{91} - 20 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(520, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
520.2.f.a $10$ $4.152$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$2$$ $$q-\beta _{3}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
520.2.f.b $10$ $4.152$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$3$$ $$-2$$ $$q-\beta _{3}q^{3}-\beta _{6}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(520, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(520, [\chi]) \cong$$