# Properties

 Label 80.6.j Level 80 Weight 6 Character orbit j Rep. character $$\chi_{80}(43,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 116 Newform subspaces 1 Sturm bound 72 Trace bound 0

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## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 80.j (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

 $$116q - 2q^{2} - 20q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 248q^{8} - 8748q^{9} + O(q^{10})$$ $$116q - 2q^{2} - 20q^{4} - 2q^{5} - 4q^{6} - 4q^{7} - 248q^{8} - 8748q^{9} - 66q^{10} - 4q^{11} - 308q^{12} - 4q^{13} + 972q^{15} - 1224q^{16} - 4q^{17} + 4214q^{18} - 2360q^{19} - 836q^{20} - 4q^{21} - 2440q^{22} - 4q^{23} + 972q^{24} - 884q^{26} - 12416q^{28} + 15336q^{30} - 17612q^{32} - 4q^{33} - 12520q^{34} - 8640q^{35} + 2380q^{36} - 4q^{37} + 15108q^{38} + 11864q^{40} - 41092q^{42} - 1316q^{43} + 8200q^{44} - 5766q^{45} - 35924q^{46} + 65256q^{47} + 5180q^{48} - 44378q^{50} + 10436q^{51} + 63080q^{52} + 33820q^{54} - 4q^{55} - 64684q^{56} + 972q^{57} - 66940q^{58} - 14480q^{59} + 136260q^{60} + 48076q^{61} + 109524q^{62} + 972q^{63} + 71920q^{64} - 4q^{65} + 72436q^{66} - 89260q^{67} + 36360q^{68} - 21348q^{69} + 59552q^{70} - 143848q^{71} + 179728q^{72} - 10072q^{73} - 82508q^{74} - 32272q^{75} - 128004q^{76} + 111388q^{78} + 313732q^{80} + 551116q^{81} - 282876q^{82} - 80928q^{84} - 6252q^{85} - 85324q^{86} - 282188q^{87} + 80224q^{88} + 115550q^{90} - 164724q^{91} + 474536q^{92} + 968q^{93} - 106060q^{94} + 204760q^{95} - 62264q^{96} - 4q^{97} + 50214q^{98} - 168788q^{99} + O(q^{100})$$

## 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.j.a $$116$$ $$12.831$$ None $$-2$$ $$0$$ $$-2$$ $$-4$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database