Defining parameters
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(539))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 176 | 102 | 74 |
Cusp forms | 160 | 102 | 58 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(7\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(28\) |
\(+\) | \(-\) | \(-\) | \(20\) |
\(-\) | \(+\) | \(-\) | \(24\) |
\(-\) | \(-\) | \(+\) | \(30\) |
Plus space | \(+\) | \(58\) | |
Minus space | \(-\) | \(44\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(539))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(539))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(539)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)