Defining parameters
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(102\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(289))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 86 | 75 | 11 |
Cusp forms | 68 | 60 | 8 |
Eisenstein series | 18 | 15 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(17\) | Dim |
---|---|
\(+\) | \(32\) |
\(-\) | \(28\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(289))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(289))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(289)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)