Defining parameters
Level: | \( N \) | = | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(57))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 276 | 194 | 82 |
Cusp forms | 204 | 162 | 42 |
Eisenstein series | 72 | 32 | 40 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)
We only show spaces with odd 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 \(S_{3}^{\mathrm{old}}(\Gamma_1(57))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(57)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)