Defining parameters
| Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8001.lm (of order \(63\) and degree \(36\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 127 \) |
| Character field: | \(\Q(\zeta_{63})\) | ||
| Sturm bound: | \(2048\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8001, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 37152 | 11520 | 25632 |
| Cusp forms | 36576 | 11520 | 25056 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(8001, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8001, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(381, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(889, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1143, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2667, [\chi])\)\(^{\oplus 2}\)