Defining parameters
| Level: | \( N \) | = | \( 1521 = 3^{2} \cdot 13^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 8 \) | ||
| Sturm bound: | \(170352\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1521))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1936 | 966 | 970 |
| Cusp forms | 112 | 46 | 66 |
| Eisenstein series | 1824 | 920 | 904 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 46 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1521))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(1521))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1521)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)