Defining parameters
Level: | \( N \) | = | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(77))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1740 | 1630 | 110 |
Cusp forms | 1620 | 1538 | 82 |
Eisenstein series | 120 | 92 | 28 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(77))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(77))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(77)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)