Defining parameters
| Level: | \( N \) | \(=\) | \( 15800 = 2^{3} \cdot 5^{2} \cdot 79 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 15800.ew (of order \(78\) and degree \(24\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 632 \) |
| Character field: | \(\Q(\zeta_{78})\) | ||
| Sturm bound: | \(4800\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(15800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 57888 | 36624 | 21264 |
| Cusp forms | 57312 | 36336 | 20976 |
| Eisenstein series | 576 | 288 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(15800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(15800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(15800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(632, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3160, [\chi])\)\(^{\oplus 2}\)