Defining parameters
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(495))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 368 | 82 | 286 |
Cusp forms | 352 | 82 | 270 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(11\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(42\) | \(6\) | \(36\) | \(40\) | \(6\) | \(34\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(50\) | \(10\) | \(40\) | \(48\) | \(10\) | \(38\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(46\) | \(10\) | \(36\) | \(44\) | \(10\) | \(34\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(46\) | \(6\) | \(40\) | \(44\) | \(6\) | \(38\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(48\) | \(13\) | \(35\) | \(46\) | \(13\) | \(33\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(44\) | \(11\) | \(33\) | \(42\) | \(11\) | \(31\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(44\) | \(12\) | \(32\) | \(42\) | \(12\) | \(30\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(48\) | \(14\) | \(34\) | \(46\) | \(14\) | \(32\) | \(2\) | \(0\) | \(2\) | |||
Plus space | \(+\) | \(176\) | \(35\) | \(141\) | \(168\) | \(35\) | \(133\) | \(8\) | \(0\) | \(8\) | |||||
Minus space | \(-\) | \(192\) | \(47\) | \(145\) | \(184\) | \(47\) | \(137\) | \(8\) | \(0\) | \(8\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(495))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(495)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)