Defining parameters
Level: | \( N \) | = | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(88704\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(688))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30156 | 16799 | 13357 |
Cusp forms | 28980 | 16429 | 12551 |
Eisenstein series | 1176 | 370 | 806 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(688))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(688))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(688)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 2}\)