Properties

 Label 80.2.s Level $80$ Weight $2$ Character orbit 80.s Rep. character $\chi_{80}(3,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ 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.s (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ 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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

 $$20q - 2q^{2} - 4q^{3} + 4q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 8q^{8} + 12q^{9} + O(q^{10})$$ $$20q - 2q^{2} - 4q^{3} + 4q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 8q^{8} + 12q^{9} + 2q^{10} - 4q^{11} - 12q^{15} - 8q^{16} - 4q^{17} - 26q^{18} - 8q^{19} - 8q^{20} - 4q^{21} + 12q^{22} - 4q^{23} - 12q^{24} - 20q^{26} - 16q^{27} + 28q^{28} + 36q^{30} + 28q^{32} - 4q^{33} + 24q^{34} + 20q^{35} - 4q^{36} + 24q^{38} + 32q^{40} - 16q^{42} - 40q^{44} - 18q^{45} + 12q^{46} + 24q^{47} + 20q^{48} - 6q^{50} + 4q^{51} + 16q^{52} - 4q^{53} - 4q^{54} - 4q^{55} + 20q^{56} - 12q^{57} + 48q^{58} + 16q^{59} + 12q^{61} - 36q^{62} - 12q^{63} + 16q^{64} - 4q^{65} + 4q^{66} - 56q^{68} - 28q^{69} - 52q^{70} + 24q^{71} - 64q^{72} - 8q^{73} - 36q^{74} + 4q^{75} - 4q^{76} - 32q^{77} - 28q^{78} - 76q^{80} - 20q^{81} + 40q^{82} + 36q^{83} + 48q^{84} + 8q^{85} - 28q^{86} + 52q^{87} - 16q^{88} - 6q^{90} + 12q^{91} - 4q^{92} - 28q^{94} + 40q^{95} - 56q^{96} - 4q^{97} - 78q^{98} + 20q^{99} + O(q^{100})$$

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.s.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$-4$$ $$-4$$ $$-6$$ $$q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
80.2.s.b $$18$$ $$0.639$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$2$$ $$2$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots$$