Properties

Label 32.6.g
Level 32
Weight 6
Character orbit g
Rep. character \(\chi_{32}(5,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 76
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(32, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 76 76 0
Eisenstein series 8 8 0

Trace form

\( 76q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} + O(q^{10}) \) \( 76q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} - 204q^{10} - 4q^{11} - 1588q^{12} - 4q^{13} + 2476q^{14} + 4176q^{16} - 1624q^{18} - 4q^{19} - 7604q^{20} - 4q^{21} - 12384q^{22} + 1668q^{23} + 21456q^{24} - 4q^{25} + 12976q^{26} - 7468q^{27} - 2184q^{28} - 4q^{29} - 32316q^{30} + 23056q^{31} - 18584q^{32} - 8q^{33} - 6256q^{34} - 4780q^{35} + 65584q^{36} - 4q^{37} + 404q^{38} - 44908q^{39} - 28952q^{40} - 4q^{41} - 53624q^{42} + 32068q^{43} + 3716q^{44} + 968q^{45} + 63324q^{46} + 112368q^{48} - 4524q^{50} - 19912q^{51} + 18468q^{52} - 49460q^{53} + 1312q^{54} + 110044q^{55} - 80984q^{56} - 4q^{57} - 84576q^{58} - 28964q^{59} - 46088q^{60} + 96156q^{61} + 63480q^{62} - 158768q^{63} - 49192q^{64} - 8q^{65} - 145012q^{66} - 61164q^{67} - 151216q^{68} - 44644q^{69} - 56296q^{70} + 143836q^{71} + 27092q^{72} - 4q^{73} + 213100q^{74} + 205744q^{75} + 255996q^{76} - 14900q^{77} + 83508q^{78} - 97096q^{80} + 435196q^{82} - 329244q^{83} + 597472q^{84} + 12496q^{85} + 269888q^{86} - 282188q^{87} - 199840q^{88} - 4q^{89} - 706840q^{90} + 200108q^{91} - 650328q^{92} - 976q^{93} - 261592q^{94} + 577592q^{95} - 501376q^{96} - 8q^{97} - 395624q^{98} + 338544q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
32.6.g.a \(76\) \(5.132\) None \(-4\) \(-4\) \(-4\) \(-4\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database