Defining parameters
| Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2401.g (of order \(21\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
| Character field: | \(\Q(\zeta_{21})\) | ||
| Sturm bound: | \(457\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2401, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3084 | 2196 | 888 |
| Cusp forms | 2412 | 1836 | 576 |
| Eisenstein series | 672 | 360 | 312 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2401, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(2401, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2401, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(343, [\chi])\)\(^{\oplus 2}\)