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Properties

Label 800.6.bq
Level $800$
Weight $6$
Character orbit 800.bq
Rep. character $\chi_{800}(63,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1200$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
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 1200 3664
Cusp forms 4736 1200 3536
Eisenstein series 128 0 128

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q - 244 q^{13} + 1212 q^{17} - 9348 q^{25} - 18864 q^{33} + 18820 q^{37} - 30780 q^{45} - 37468 q^{53} - 82592 q^{57} - 5084 q^{65} + 1972 q^{73} - 241008 q^{77} + 1968300 q^{81} - 315488 q^{85} + 526740 q^{89} + 353040 q^{93} - 1827324 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)