Defining parameters
| Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7168.ca (of order \(128\) and degree \(64\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 512 \) |
| Character field: | \(\Q(\zeta_{128})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2048\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7168, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 65792 | 0 | 65792 |
| Cusp forms | 65280 | 0 | 65280 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(7168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7168, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1024, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3584, [\chi])\)\(^{\oplus 2}\)