Defining parameters
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1104))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 204 | 22 | 182 |
Cusp forms | 181 | 22 | 159 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(19\) | \(2\) | \(17\) | \(17\) | \(2\) | \(15\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(32\) | \(4\) | \(28\) | \(29\) | \(4\) | \(25\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(23\) | \(3\) | \(20\) | \(20\) | \(3\) | \(17\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(28\) | \(1\) | \(27\) | \(25\) | \(1\) | \(24\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(26\) | \(4\) | \(22\) | \(23\) | \(4\) | \(19\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(25\) | \(2\) | \(23\) | \(22\) | \(2\) | \(20\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(22\) | \(2\) | \(20\) | \(19\) | \(2\) | \(17\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(29\) | \(4\) | \(25\) | \(26\) | \(4\) | \(22\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(94\) | \(7\) | \(87\) | \(83\) | \(7\) | \(76\) | \(11\) | \(0\) | \(11\) | |||||
Minus space | \(-\) | \(110\) | \(15\) | \(95\) | \(98\) | \(15\) | \(83\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1104))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1104)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)