Defining parameters
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(352\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(688))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 270 | 63 | 207 |
Cusp forms | 258 | 63 | 195 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(43\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(17\) |
\(+\) | \(-\) | $-$ | \(14\) |
\(-\) | \(+\) | $-$ | \(16\) |
\(-\) | \(-\) | $+$ | \(16\) |
Plus space | \(+\) | \(33\) | |
Minus space | \(-\) | \(30\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(688))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(688))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(688)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(344))\)\(^{\oplus 2}\)