Defining parameters
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 23 \) | ||
Sturm bound: | \(264\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1089))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 50 | 106 |
Cusp forms | 109 | 41 | 68 |
Eisenstein series | 47 | 9 | 38 |
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 | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(36\) | \(6\) | \(30\) | \(25\) | \(6\) | \(19\) | \(11\) | \(0\) | \(11\) | |||
\(+\) | \(-\) | \(-\) | \(42\) | \(12\) | \(30\) | \(30\) | \(12\) | \(18\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(+\) | \(-\) | \(42\) | \(17\) | \(25\) | \(30\) | \(13\) | \(17\) | \(12\) | \(4\) | \(8\) | |||
\(-\) | \(-\) | \(+\) | \(36\) | \(15\) | \(21\) | \(24\) | \(10\) | \(14\) | \(12\) | \(5\) | \(7\) | |||
Plus space | \(+\) | \(72\) | \(21\) | \(51\) | \(49\) | \(16\) | \(33\) | \(23\) | \(5\) | \(18\) | ||||
Minus space | \(-\) | \(84\) | \(29\) | \(55\) | \(60\) | \(25\) | \(35\) | \(24\) | \(4\) | \(20\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1089))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1089)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)