Defining parameters
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 27 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(912))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 812 | 90 | 722 |
Cusp forms | 788 | 90 | 698 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(12\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(10\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(13\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(9\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(12\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(12\) |
Plus space | \(+\) | \(43\) | ||
Minus space | \(-\) | \(47\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(912))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(912))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(912)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)