Defining parameters
| Level: | \( N \) | \(=\) | \( 8352 = 2^{5} \cdot 3^{2} \cdot 29 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8352.gf (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2088 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8352, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 17472 | 4368 | 13104 |
| Cusp forms | 17088 | 4272 | 12816 |
| Eisenstein series | 384 | 96 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(8352, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8352, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(2088, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4176, [\chi])\)\(^{\oplus 2}\)