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Properties

Label 800.6.bp
Level $800$
Weight $6$
Character orbit 800.bp
Rep. character $\chi_{800}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1184$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4864 1216 3648
Cusp forms 4736 1184 3552
Eisenstein series 128 32 96

Trace form

\( 1184 q + 16 q^{3} - 20 q^{9} + O(q^{10}) \) \( 1184 q + 16 q^{3} - 20 q^{9} + 12 q^{11} + 388 q^{17} + 20 q^{19} + 3100 q^{25} + 988 q^{27} + 956 q^{33} - 4760 q^{35} - 12 q^{41} + 1328 q^{43} + 32 q^{51} - 988 q^{57} + 20 q^{59} - 17700 q^{65} + 89272 q^{67} + 25164 q^{73} - 127720 q^{75} + 1732092 q^{81} - 126424 q^{83} + 877880 q^{89} + 12 q^{91} + 448284 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)