Defining parameters
| Level: | \( N \) | = | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | = | \( 8 \) |
| Nonzero newspaces: | \( 20 \) | ||
| Sturm bound: | \(27648\) | ||
| Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(252))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12336 | 5402 | 6934 |
| Cusp forms | 11856 | 5310 | 6546 |
| Eisenstein series | 480 | 92 | 388 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(252))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)