Defining parameters
Level: | \( N \) | \(=\) | \( 5776 = 2^{4} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5776.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 57 \) | ||
Sturm bound: | \(1520\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5776))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 820 | 179 | 641 |
Cusp forms | 701 | 162 | 539 |
Eisenstein series | 119 | 17 | 102 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(19\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(40\) |
\(+\) | \(-\) | $-$ | \(45\) |
\(-\) | \(+\) | $-$ | \(41\) |
\(-\) | \(-\) | $+$ | \(36\) |
Plus space | \(+\) | \(76\) | |
Minus space | \(-\) | \(86\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5776))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5776))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5776)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\)\(^{\oplus 2}\)