Defining parameters
Level: | \( N \) | \(=\) | \( 6633 = 3^{2} \cdot 11 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6633.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(1632\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6633))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 824 | 274 | 550 |
Cusp forms | 809 | 274 | 535 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | \(67\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(29\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(25\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(29\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(25\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(43\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(40\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(38\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(45\) |
Plus space | \(+\) | \(132\) | ||
Minus space | \(-\) | \(142\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6633))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6633))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6633)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(603))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(737))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2211))\)\(^{\oplus 2}\)