# Properties

 Label 20.2.e Level $20$ Weight $2$ Character orbit 20.e Rep. character $\chi_{20}(3,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 20.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(20, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

## Trace form

 $$2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + O(q^{10})$$ $$2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 6 q^{10} - 2 q^{13} - 8 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{25} + 4 q^{26} + 8 q^{32} + 12 q^{36} - 14 q^{37} - 4 q^{40} - 16 q^{41} + 6 q^{45} - 14 q^{50} - 4 q^{52} + 18 q^{53} + 8 q^{58} + 24 q^{61} + 2 q^{65} - 12 q^{68} - 12 q^{72} - 22 q^{73} + 16 q^{80} - 18 q^{81} + 16 q^{82} - 18 q^{85} + 6 q^{90} + 26 q^{97} + 14 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(20, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.2.e.a $2$ $0.160$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$$