Defining parameters
Level: | \( N \) | \(=\) | \( 578 = 2 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 578.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(153\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(578))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 94 | 23 | 71 |
Cusp forms | 59 | 23 | 36 |
Eisenstein series | 35 | 0 | 35 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(+\) | $-$ | \(8\) |
\(-\) | \(-\) | $+$ | \(3\) |
Plus space | \(+\) | \(8\) | |
Minus space | \(-\) | \(15\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(578))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(578))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(578)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)