Defining parameters
| Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8619.fn (of order \(624\) and degree \(192\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2873 \) |
| Character field: | \(\Q(\zeta_{624})\) | ||
| Sturm bound: | \(2184\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8619, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 210432 | 104832 | 105600 |
| Cusp forms | 208896 | 104832 | 104064 |
| Eisenstein series | 1536 | 0 | 1536 |
Decomposition of \(S_{2}^{\mathrm{new}}(8619, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8619, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8619, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2873, [\chi])\)\(^{\oplus 2}\)