Defining parameters
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(322))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52 | 11 | 41 |
Cusp forms | 45 | 11 | 34 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(3\) |
Plus space | \(+\) | \(4\) | ||
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(322))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(322))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(322)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)