Properties

Label 40.6.k
Level 40
Weight 6
Character orbit k
Rep. character \(\chi_{40}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 56
Newform subspaces 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 40.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(40, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56q - 2q^{2} - 4q^{3} + 176q^{6} + 244q^{8} + O(q^{10}) \) \( 56q - 2q^{2} - 4q^{3} + 176q^{6} + 244q^{8} - 570q^{10} - 8q^{11} - 308q^{12} + 456q^{16} - 408q^{17} + 3370q^{18} + 1360q^{20} - 3148q^{22} - 3120q^{25} - 5084q^{26} + 968q^{27} - 10020q^{28} + 21100q^{30} + 7968q^{32} - 976q^{33} - 4780q^{35} + 23132q^{36} - 49524q^{38} - 58980q^{40} - 8q^{41} + 42060q^{42} + 1308q^{43} + 42416q^{46} + 93776q^{48} - 94010q^{50} + 20872q^{51} - 67180q^{52} - 43384q^{56} + 968q^{57} + 86100q^{58} + 118180q^{60} + 6240q^{62} + 17680q^{65} - 41128q^{66} + 89252q^{67} - 158164q^{68} + 116980q^{70} + 1180q^{72} - 25184q^{73} - 127740q^{75} + 41592q^{76} - 161440q^{78} - 167360q^{80} - 67792q^{81} + 23412q^{82} - 126444q^{83} - 192704q^{86} + 100176q^{88} - 82330q^{90} + 329432q^{91} + 226020q^{92} + 358176q^{96} + 212576q^{97} + 65834q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
40.6.k.a \(56\) \(6.415\) None \(-2\) \(-4\) \(0\) \(0\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database