# Properties

 Label 80.6.s Level 80 Weight 6 Character orbit s Rep. character $$\chi_{80}(3,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 116 Newform subspaces 1 Sturm bound 72 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 80.s (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(80, [\chi])$$.

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

## Trace form

 $$116q - 2q^{2} - 4q^{3} + 20q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 248q^{8} + 8748q^{9} + O(q^{10})$$ $$116q - 2q^{2} - 4q^{3} + 20q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 248q^{8} + 8748q^{9} + 62q^{10} - 4q^{11} - 1280q^{12} - 972q^{15} - 1224q^{16} - 4q^{17} - 4346q^{18} + 2360q^{19} + 832q^{20} - 4q^{21} - 3148q^{22} - 4q^{23} - 972q^{24} - 884q^{26} - 976q^{27} + 16508q^{28} + 19836q^{30} - 7972q^{32} - 4q^{33} + 12520q^{34} + 3860q^{35} + 2380q^{36} - 12256q^{38} + 16192q^{40} + 38424q^{42} - 8200q^{44} - 6738q^{45} - 35924q^{46} - 65256q^{47} + 17620q^{48} + 24194q^{50} + 10436q^{51} - 34384q^{52} - 4q^{53} - 33820q^{54} - 4q^{55} - 64684q^{56} - 972q^{57} - 30632q^{58} + 14480q^{59} + 1200q^{60} + 48076q^{61} - 6116q^{62} - 972q^{63} - 71920q^{64} - 4q^{65} + 72436q^{66} + 119464q^{68} + 21348q^{69} - 141252q^{70} - 143848q^{71} - 130864q^{72} + 10072q^{73} + 82508q^{74} + 160004q^{75} - 128004q^{76} - 67232q^{77} - 253108q^{78} - 171436q^{80} + 551116q^{81} - 152200q^{82} + 126436q^{83} + 80928q^{84} + 6248q^{85} - 85324q^{86} - 282188q^{87} - 247536q^{88} + 275094q^{90} - 164724q^{91} + 336476q^{92} + 106060q^{94} - 204760q^{95} - 62264q^{96} - 4q^{97} + 110122q^{98} + 168788q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(80, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
80.6.s.a $$116$$ $$12.831$$ None $$-2$$ $$-4$$ $$-2$$ $$-4$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database