# Properties

 Label 80.2.q Level $80$ Weight $2$ Character orbit 80.q Rep. character $\chi_{80}(29,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ Newform subspaces $3$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

## Trace form

 $$20q - 4q^{4} - 2q^{5} - 4q^{6} + O(q^{10})$$ $$20q - 4q^{4} - 2q^{5} - 4q^{6} - 8q^{10} - 4q^{11} - 4q^{14} - 4q^{15} - 12q^{19} - 16q^{20} - 16q^{21} - 16q^{24} + 32q^{26} - 4q^{29} - 24q^{30} + 16q^{31} + 32q^{34} - 24q^{35} + 68q^{36} + 24q^{40} + 16q^{44} + 14q^{45} + 4q^{46} - 12q^{49} + 36q^{50} + 8q^{54} - 56q^{56} + 12q^{59} + 48q^{60} - 20q^{61} - 16q^{64} - 12q^{65} - 96q^{66} + 20q^{70} - 24q^{74} + 36q^{75} - 96q^{76} + 48q^{79} - 8q^{80} + 4q^{81} - 80q^{84} + 8q^{85} - 52q^{86} - 84q^{90} - 16q^{91} + 4q^{94} + 20q^{95} + 56q^{96} + 76q^{99} + O(q^{100})$$

## 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.q.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$2$$ $$2$$ $$0$$ $$q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots$$
80.2.q.b $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$-2$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots$$
80.2.q.c $$16$$ $$0.639$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$$