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Properties

Label 800.4.bq
Level $800$
Weight $4$
Character orbit 800.bq
Rep. character $\chi_{800}(63,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(800, [\chi])\).

Total New Old
Modular forms 2944 720 2224
Cusp forms 2816 720 2096
Eisenstein series 128 0 128

Trace form

\( 720 q + O(q^{10}) \) \( 720 q - 92 q^{13} - 156 q^{17} + 132 q^{25} + 48 q^{33} - 660 q^{37} - 180 q^{45} - 244 q^{53} + 1696 q^{57} - 644 q^{65} - 1524 q^{73} + 3504 q^{77} + 14580 q^{81} + 11232 q^{85} - 660 q^{89} - 12240 q^{93} + 15132 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

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