Defining parameters
Level: | \( N \) | = | \( 159 = 3 \cdot 53 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(3744\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(159))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1040 | 753 | 287 |
Cusp forms | 833 | 649 | 184 |
Eisenstein series | 207 | 104 | 103 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(159))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(159)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)