Defining parameters
Level: | \( N \) | \(=\) | \( 5808 = 2^{4} \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5808.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 67 \) | ||
Sturm bound: | \(2112\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5808))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1128 | 109 | 1019 |
Cusp forms | 985 | 109 | 876 |
Eisenstein series | 143 | 0 | 143 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(12\) |
\(+\) | \(+\) | \(-\) | $-$ | \(15\) |
\(+\) | \(-\) | \(+\) | $-$ | \(18\) |
\(+\) | \(-\) | \(-\) | $+$ | \(10\) |
\(-\) | \(+\) | \(+\) | $-$ | \(12\) |
\(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(-\) | \(-\) | $-$ | \(15\) |
Plus space | \(+\) | \(49\) | ||
Minus space | \(-\) | \(60\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5808))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5808))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5808)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2904))\)\(^{\oplus 2}\)