Defining parameters
Level: | \( N \) | = | \( 51 = 3 \cdot 17 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(51))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 87 | 41 |
Cusp forms | 65 | 55 | 10 |
Eisenstein series | 63 | 32 | 31 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(51)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)