Properties

Label 320.6.bd
Level 320
Weight 6
Character orbit bd
Rep. character \(\chi_{320}(43,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 1904
Sturm bound 288

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(320, [\chi])\).

Total New Old
Modular forms 1936 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

Trace form

\( 1904q - 8q^{2} - 8q^{3} - 8q^{5} - 16q^{6} - 8q^{7} - 8q^{8} + O(q^{10}) \) \( 1904q - 8q^{2} - 8q^{3} - 8q^{5} - 16q^{6} - 8q^{7} - 8q^{8} - 8q^{10} - 16q^{11} - 3176q^{12} - 8q^{13} + 4960q^{14} - 8q^{15} - 16q^{16} - 8q^{18} - 8q^{20} - 16q^{21} + 11160q^{22} - 8q^{23} - 20880q^{24} - 8q^{25} - 16q^{26} - 8q^{27} - 8q^{28} - 64632q^{30} - 32q^{31} - 8q^{32} + 512q^{34} - 8q^{35} - 16q^{36} - 8q^{37} + 68816q^{38} + 182608q^{40} - 16q^{41} - 8q^{42} - 8q^{43} - 1952q^{45} - 16q^{46} - 16q^{47} + 224736q^{48} + 128016q^{50} - 41776q^{51} - 8q^{52} - 8q^{53} - 8q^{55} - 258736q^{56} - 8q^{57} + 195128q^{58} - 97504q^{60} - 16q^{61} - 264q^{62} - 16q^{65} + 254864q^{66} - 8q^{67} - 295280q^{68} + 89280q^{69} - 8q^{70} + 287664q^{71} + 359872q^{72} - 8q^{73} - 8q^{75} - 268496q^{76} - 8q^{77} - 889360q^{78} + 355360q^{79} - 8q^{80} - 16q^{81} + 870392q^{82} - 8q^{83} + 24992q^{85} - 16q^{86} + 564360q^{87} - 622960q^{88} - 8q^{90} - 16q^{91} - 228712q^{92} - 1952q^{93} - 512q^{94} - 16q^{95} - 16q^{96} - 811248q^{98} - 679040q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database