Defining parameters
| Level: | \( N \) | \(=\) | \( 15800 = 2^{3} \cdot 5^{2} \cdot 79 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 15800.gm (of order \(260\) and degree \(96\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1975 \) |
| Character field: | \(\Q(\zeta_{260})\) | ||
| Sturm bound: | \(4800\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(15800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 231168 | 57600 | 173568 |
| Cusp forms | 229632 | 57600 | 172032 |
| Eisenstein series | 1536 | 0 | 1536 |
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
\( S_{2}^{\mathrm{old}}(15800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1975, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7900, [\chi])\)\(^{\oplus 2}\)