Properties

Label 80.6.q
Level 80
Weight 6
Character orbit q
Rep. character \(\chi_{80}(29,\cdot)\)
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.q (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

\( 116q - 4q^{4} - 2q^{5} - 4q^{6} + O(q^{10}) \) \( 116q - 4q^{4} - 2q^{5} - 4q^{6} + 532q^{10} - 4q^{11} + 1108q^{14} - 4q^{15} + 1216q^{16} + 2356q^{19} + 824q^{20} - 976q^{21} - 2864q^{24} - 12104q^{26} - 4q^{29} + 736q^{30} + 23056q^{31} - 38304q^{34} - 3864q^{35} - 20588q^{36} + 15144q^{40} - 25536q^{44} + 6734q^{45} - 36052q^{46} + 220884q^{49} + 56116q^{50} - 9472q^{51} - 104360q^{54} - 2552q^{56} + 14476q^{59} + 1008q^{60} - 48084q^{61} + 72944q^{64} - 27692q^{65} - 56736q^{66} - 23296q^{69} + 135260q^{70} - 186128q^{74} - 33244q^{75} - 35824q^{76} + 427312q^{79} - 129128q^{80} - 551132q^{81} - 418448q^{84} + 6248q^{85} + 177516q^{86} + 449576q^{90} - 231952q^{91} + 607356q^{94} + 38420q^{95} - 440264q^{96} + 406924q^{99} + O(q^{100}) \)

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.q.a \(116\) \(12.831\) None \(0\) \(0\) \(-2\) \(0\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database