Defining parameters
| Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 800.bi (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
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
\( S_{3}^{\mathrm{old}}(800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)