Defining parameters
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 49 \) | ||
Sturm bound: | \(1740\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7569))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 930 | 352 | 578 |
Cusp forms | 811 | 325 | 486 |
Eisenstein series | 119 | 27 | 92 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(61\) |
\(+\) | \(-\) | \(-\) | \(75\) |
\(-\) | \(+\) | \(-\) | \(98\) |
\(-\) | \(-\) | \(+\) | \(91\) |
Plus space | \(+\) | \(152\) | |
Minus space | \(-\) | \(173\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7569))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7569))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7569)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2523))\)\(^{\oplus 2}\)