Defining parameters
| Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(4\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(4))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5 | 0 | 5 |
| Cusp forms | 2 | 0 | 2 |
| Eisenstein series | 3 | 0 | 3 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)