Defining parameters
| Level: | \( N \) | = | \( 567 = 3^{4} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Newform subspaces: | \( 11 \) | ||
| Sturm bound: | \(23328\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(567))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 681 | 302 | 379 |
| Cusp forms | 33 | 22 | 11 |
| Eisenstein series | 648 | 280 | 368 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 22 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(567))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(567))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(567)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)