Defining parameters
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(585))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 428 | 100 | 328 |
Cusp forms | 412 | 100 | 312 |
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.
\(3\) | \(5\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(11\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(9\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(11\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(9\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(15\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(14\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(14\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(17\) |
Plus space | \(+\) | \(48\) | ||
Minus space | \(-\) | \(52\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(585))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(585))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(585)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 2}\)