Defining parameters
Level: | \( N \) | \(=\) | \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5796.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(2304\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5796))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1176 | 56 | 1120 |
Cusp forms | 1129 | 56 | 1073 |
Eisenstein series | 47 | 0 | 47 |
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 | Dim |
---|---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(6\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(10\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(10\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(24\) | |||
Minus space | \(-\) | \(32\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5796))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5796))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5796)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\)\(^{\oplus 2}\)