Defining parameters
Level: | \( N \) | \(=\) | \( 9633 = 3 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9633.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 49 \) | ||
Sturm bound: | \(2426\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9633))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1240 | 466 | 774 |
Cusp forms | 1185 | 466 | 719 |
Eisenstein series | 55 | 0 | 55 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(13\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(60\) |
\(+\) | \(+\) | \(-\) | $-$ | \(53\) |
\(+\) | \(-\) | \(+\) | $-$ | \(57\) |
\(+\) | \(-\) | \(-\) | $+$ | \(63\) |
\(-\) | \(+\) | \(+\) | $-$ | \(67\) |
\(-\) | \(+\) | \(-\) | $+$ | \(46\) |
\(-\) | \(-\) | \(+\) | $+$ | \(51\) |
\(-\) | \(-\) | \(-\) | $-$ | \(69\) |
Plus space | \(+\) | \(220\) | ||
Minus space | \(-\) | \(246\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9633))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9633))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9633)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(741))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3211))\)\(^{\oplus 2}\)