Defining parameters
Level: | \( N \) | = | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 20 \) | ||
Sturm bound: | \(88704\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(387))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 39144 | 30872 | 8272 |
Cusp forms | 38472 | 30504 | 7968 |
Eisenstein series | 672 | 368 | 304 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(387))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)