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Properties

Label 800.3.bo
Level $800$
Weight $3$
Character orbit 800.bo
Rep. character $\chi_{800}(33,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 800.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(800, [\chi])\).

Total New Old
Modular forms 1984 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 24 q^{13} + 24 q^{17} - 72 q^{25} - 96 q^{33} - 40 q^{37} + 120 q^{45} + 344 q^{53} - 64 q^{57} + 360 q^{65} + 296 q^{73} + 96 q^{77} + 1080 q^{81} + 832 q^{85} - 600 q^{89} + 96 q^{93} - 600 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)