# Properties

 Label 80.2.n Level $80$ Weight $2$ Character orbit 80.n Rep. character $\chi_{80}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 80.n (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(80, [\chi])$$.

Total New Old
Modular forms 36 6 30
Cusp forms 12 6 6
Eisenstein series 24 0 24

## Trace form

 $$6 q + O(q^{10})$$ $$6 q - 6 q^{13} - 6 q^{17} - 24 q^{21} - 6 q^{25} + 24 q^{33} + 30 q^{37} + 24 q^{41} + 30 q^{45} - 18 q^{53} - 48 q^{57} - 42 q^{65} - 18 q^{73} + 24 q^{77} + 18 q^{81} - 6 q^{85} - 24 q^{93} - 18 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(80, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.2.n.a $2$ $0.639$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots$$
80.2.n.b $4$ $0.639$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(80, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(80, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$