Defining parameters
| Level: | \( N \) | = | \( 4 = 2^{2} \) |
| Weight: | \( k \) | = | \( 8 \) |
| Nonzero newspaces: | \( 0 \) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(8\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(4))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5 | 0 | 5 |
| Cusp forms | 2 | 0 | 2 |
| Eisenstein series | 3 | 0 | 3 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(4)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)