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 | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(6\) |
\(+\) | \(+\) | \(-\) | $-$ | \(10\) |
\(+\) | \(-\) | \(+\) | $-$ | \(10\) |
\(+\) | \(-\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(+\) | $-$ | \(13\) |
\(-\) | \(+\) | \(-\) | $+$ | \(11\) |
\(-\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(-\) | \(-\) | $-$ | \(14\) |
Plus space | \(+\) | \(35\) | ||
Minus space | \(-\) | \(47\) |
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
\( S_{6}^{\mathrm{old}}(\Gamma_0(495)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)