Defining parameters
| Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 112.m (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(128\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(112, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 228 | 168 | 60 |
| Cusp forms | 220 | 168 | 52 |
| Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(112, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{8}^{\mathrm{old}}(112, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)