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Properties

Label 160.6.u
Level $160$
Weight $6$
Character orbit 160.u
Rep. character $\chi_{160}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $472$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(160, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 496 q^{8} + O(q^{10}) \) \( 472 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 496 q^{8} + 1064 q^{10} - 8 q^{11} + 1580 q^{12} - 4 q^{13} + 256 q^{14} - 8 q^{15} - 8 q^{16} + 124 q^{18} - 4720 q^{19} - 1656 q^{20} - 8 q^{21} + 5580 q^{22} - 16160 q^{24} - 4 q^{25} - 8 q^{26} - 976 q^{27} + 4092 q^{28} + 63488 q^{30} + 25576 q^{32} - 8 q^{33} + 27640 q^{34} + 17272 q^{35} - 8 q^{36} - 4 q^{37} - 2860 q^{38} - 31184 q^{40} - 8 q^{41} + 59540 q^{42} - 1316 q^{43} + 9680 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 201944 q^{48} - 1018024 q^{49} - 132 q^{50} + 20872 q^{51} - 128136 q^{52} - 4 q^{53} - 154280 q^{54} + 110044 q^{55} - 129368 q^{56} - 8 q^{57} + 97564 q^{58} + 4092 q^{60} - 96168 q^{61} - 103160 q^{62} + 134456 q^{63} - 234960 q^{64} - 8 q^{65} + 109992 q^{66} - 89260 q^{67} - 155832 q^{68} + 1944 q^{69} - 132540 q^{70} - 143848 q^{71} - 311016 q^{72} - 8 q^{73} + 968 q^{75} - 12488 q^{76} + 67224 q^{77} + 747632 q^{78} + 376632 q^{80} - 67796 q^{82} - 126444 q^{83} + 134456 q^{84} - 4 q^{85} - 91048 q^{86} + 564360 q^{87} + 167304 q^{88} - 725172 q^{90} - 8 q^{91} + 118444 q^{92} + 968 q^{93} + 238240 q^{94} + 304152 q^{96} - 8 q^{97} + 971064 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

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