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Properties

Label 800.6.v
Level $800$
Weight $6$
Character orbit 800.v
Rep. character $\chi_{800}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1432$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 2424 1448 976
Cusp forms 2376 1432 944
Eisenstein series 48 16 32

Trace form

\( 1432 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 496 q^{8} + O(q^{10}) \) \( 1432 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 496 q^{8} - 8 q^{11} - 1580 q^{12} + 4 q^{13} + 256 q^{14} - 8 q^{16} - 124 q^{18} + 9440 q^{19} - 8 q^{21} - 5580 q^{22} + 32320 q^{24} - 8 q^{26} + 976 q^{27} - 4092 q^{28} - 25576 q^{32} + 8 q^{33} - 55280 q^{34} - 8 q^{36} + 4 q^{37} + 2860 q^{38} - 8 q^{41} - 59540 q^{42} + 1316 q^{43} - 19360 q^{44} - 8 q^{46} + 8 q^{47} + 201944 q^{48} - 3322984 q^{49} - 41768 q^{51} + 128136 q^{52} + 4 q^{53} + 308560 q^{54} - 64688 q^{56} + 8 q^{57} - 97564 q^{58} + 192312 q^{61} + 103160 q^{62} - 134456 q^{63} - 117480 q^{64} - 220008 q^{66} + 89260 q^{67} + 155832 q^{68} + 1944 q^{69} + 287672 q^{71} + 311016 q^{72} + 8 q^{73} + 24952 q^{76} - 67224 q^{77} - 747632 q^{78} + 67796 q^{82} + 126444 q^{83} + 134456 q^{84} + 182072 q^{86} - 564360 q^{87} - 167304 q^{88} - 8 q^{91} - 118444 q^{92} - 968 q^{93} - 476480 q^{94} - 608328 q^{96} + 8 q^{97} - 971064 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)