Defining parameters
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3864))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 784 | 68 | 716 |
Cusp forms | 753 | 68 | 685 |
Eisenstein series | 31 | 0 | 31 |
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. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(28\) | |||
Minus space | \(-\) | \(40\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3864))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3864))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 2}\)