Defining parameters
| Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9408.dx (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 588 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(3584\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9408, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 21792 | 5424 | 16368 |
| Cusp forms | 21216 | 5328 | 15888 |
| Eisenstein series | 576 | 96 | 480 |
Decomposition of \(S_{2}^{\mathrm{new}}(9408, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9408, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9408, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2352, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4704, [\chi])\)\(^{\oplus 2}\)