Defining parameters
Level: | \( N \) | \(=\) | \( 862 = 2 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 862.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(862))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 110 | 35 | 75 |
Cusp forms | 107 | 35 | 72 |
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.
\(2\) | \(431\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(8\) |
\(+\) | \(-\) | $-$ | \(10\) |
\(-\) | \(+\) | $-$ | \(9\) |
\(-\) | \(-\) | $+$ | \(8\) |
Plus space | \(+\) | \(16\) | |
Minus space | \(-\) | \(19\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(862))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(862))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(862)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 2}\)