Defining parameters
| Level: | \( N \) | = | \( 58 = 2 \cdot 29 \) |
| Weight: | \( k \) | = | \( 4 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 8 \) | ||
| Sturm bound: | \(840\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(58))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 343 | 105 | 238 |
| Cusp forms | 287 | 105 | 182 |
| Eisenstein series | 56 | 0 | 56 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)