Defining parameters
| Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3136.bq (of order \(24\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 224 \) |
| Character field: | \(\Q(\zeta_{24})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(896\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3712 | 0 | 3712 |
| Cusp forms | 3456 | 0 | 3456 |
| Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)