Defining parameters
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(966))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 200 | 21 | 179 |
Cusp forms | 185 | 21 | 164 |
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.
\(2\) | \(3\) | \(7\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(8\) | \(1\) | \(7\) | \(8\) | \(1\) | \(7\) | \(0\) | \(0\) | \(0\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(15\) | \(2\) | \(13\) | \(14\) | \(2\) | \(12\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(15\) | \(1\) | \(14\) | \(14\) | \(1\) | \(13\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(12\) | \(2\) | \(10\) | \(11\) | \(2\) | \(9\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(14\) | \(2\) | \(12\) | \(13\) | \(2\) | \(11\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(11\) | \(1\) | \(10\) | \(10\) | \(1\) | \(9\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(13\) | \(0\) | \(13\) | \(12\) | \(0\) | \(12\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(12\) | \(3\) | \(9\) | \(11\) | \(3\) | \(8\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(12\) | \(2\) | \(10\) | \(11\) | \(2\) | \(9\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(14\) | \(0\) | \(14\) | \(13\) | \(0\) | \(13\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(13\) | \(1\) | \(12\) | \(12\) | \(1\) | \(11\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(11\) | \(1\) | \(10\) | \(10\) | \(1\) | \(9\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(12\) | \(0\) | \(12\) | \(11\) | \(0\) | \(11\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(14\) | \(2\) | \(12\) | \(13\) | \(2\) | \(11\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(13\) | \(3\) | \(10\) | \(12\) | \(3\) | \(9\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(11\) | \(0\) | \(11\) | \(10\) | \(0\) | \(10\) | \(1\) | \(0\) | \(1\) | |||
Plus space | \(+\) | \(94\) | \(5\) | \(89\) | \(87\) | \(5\) | \(82\) | \(7\) | \(0\) | \(7\) | ||||||
Minus space | \(-\) | \(106\) | \(16\) | \(90\) | \(98\) | \(16\) | \(82\) | \(8\) | \(0\) | \(8\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(966))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(966))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(966)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)