Defining parameters
Level: | \( N \) | \(=\) | \( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5775.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 68 \) | ||
Sturm bound: | \(1920\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(2\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5775))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 984 | 188 | 796 |
Cusp forms | 937 | 188 | 749 |
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.
\(3\) | \(5\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(10\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(13\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(13\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(10\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(15\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(15\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(13\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(13\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(15\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(15\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(9\) |
Plus space | \(+\) | \(76\) | |||
Minus space | \(-\) | \(112\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5775))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5775))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\)\(^{\oplus 2}\)