Defining parameters
Level: | \( N \) | = | \( 58 = 2 \cdot 29 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(1680\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(58))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 763 | 243 | 520 |
Cusp forms | 707 | 243 | 464 |
Eisenstein series | 56 | 0 | 56 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(58))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)