Defining parameters
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 40 \) | ||
Sturm bound: | \(528\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1089))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 420 | 141 | 279 |
Cusp forms | 372 | 132 | 240 |
Eisenstein series | 48 | 9 | 39 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(30\) |
\(+\) | \(-\) | $-$ | \(25\) |
\(-\) | \(+\) | $-$ | \(37\) |
\(-\) | \(-\) | $+$ | \(40\) |
Plus space | \(+\) | \(70\) | |
Minus space | \(-\) | \(62\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1089))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1089))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1089)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)