Defining parameters
Level: | \( N \) | \(=\) | \( 579 = 3 \cdot 193 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 579.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(129\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(579))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 33 | 33 |
Cusp forms | 63 | 33 | 30 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(193\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(-\) | \(11\) |
\(-\) | \(+\) | \(-\) | \(13\) |
\(-\) | \(-\) | \(+\) | \(4\) |
Plus space | \(+\) | \(9\) | |
Minus space | \(-\) | \(24\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(579))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(579))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(579)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(193))\)\(^{\oplus 2}\)