Defining parameters
| Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4704.cl (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1176 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Sturm bound: | \(1792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4704, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5472 | 1368 | 4104 |
| Cusp forms | 5280 | 1320 | 3960 |
| Eisenstein series | 192 | 48 | 144 |
Decomposition of \(S_{2}^{\mathrm{new}}(4704, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4704, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4704, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2352, [\chi])\)\(^{\oplus 2}\)