Defining parameters
Level: | \( N \) | \(=\) | \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9036.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(3024\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9036))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1524 | 103 | 1421 |
Cusp forms | 1501 | 103 | 1398 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(251\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(20\) |
\(-\) | \(+\) | \(-\) | $+$ | \(20\) |
\(-\) | \(-\) | \(+\) | $+$ | \(28\) |
\(-\) | \(-\) | \(-\) | $-$ | \(35\) |
Plus space | \(+\) | \(48\) | ||
Minus space | \(-\) | \(55\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9036))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9036))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2259))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4518))\)\(^{\oplus 2}\)