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