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Properties

Label 800.3.bd
Level $800$
Weight $3$
Character orbit 800.bd
Rep. character $\chi_{800}(111,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $232$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 800.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 992 248 744
Cusp forms 928 232 696
Eisenstein series 64 16 48

Trace form

\( 232 q + 6 q^{3} - 168 q^{9} + O(q^{10}) \) \( 232 q + 6 q^{3} - 168 q^{9} + 6 q^{11} - 14 q^{17} + 6 q^{19} - 20 q^{25} - 30 q^{27} + 30 q^{33} - 240 q^{35} + 34 q^{41} + 144 q^{43} - 1304 q^{49} - 20 q^{51} + 20 q^{57} + 6 q^{59} - 110 q^{65} - 426 q^{67} + 114 q^{73} - 90 q^{75} - 348 q^{81} - 154 q^{83} + 294 q^{89} - 288 q^{91} - 126 q^{97} - 344 q^{99} + O(q^{100}) \)

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

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