Defining parameters
| Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 112.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(128\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(112, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 116 | 0 | 116 |
| Cusp forms | 108 | 0 | 108 |
| Eisenstein series | 8 | 0 | 8 |
Decomposition of \(S_{8}^{\mathrm{old}}(112, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)