Defining parameters
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(531))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 424 | 168 | 256 |
Cusp forms | 416 | 168 | 248 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(59\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(33\) |
\(+\) | \(-\) | $-$ | \(33\) |
\(-\) | \(+\) | $-$ | \(48\) |
\(-\) | \(-\) | $+$ | \(54\) |
Plus space | \(+\) | \(87\) | |
Minus space | \(-\) | \(81\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(531))\) into newform subspaces
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(531))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(531)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)