Defining parameters
Level: | \( N \) | \(=\) | \( 2325 = 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2325.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(640\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2325))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 332 | 96 | 236 |
Cusp forms | 309 | 96 | 213 |
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.
\(3\) | \(5\) | \(31\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(39\) | \(11\) | \(28\) | \(37\) | \(11\) | \(26\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(42\) | \(11\) | \(31\) | \(39\) | \(11\) | \(28\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(44\) | \(11\) | \(33\) | \(41\) | \(11\) | \(30\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(41\) | \(15\) | \(26\) | \(38\) | \(15\) | \(23\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(44\) | \(14\) | \(30\) | \(41\) | \(14\) | \(27\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(41\) | \(8\) | \(33\) | \(38\) | \(8\) | \(30\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(39\) | \(9\) | \(30\) | \(36\) | \(9\) | \(27\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(42\) | \(17\) | \(25\) | \(39\) | \(17\) | \(22\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(160\) | \(43\) | \(117\) | \(149\) | \(43\) | \(106\) | \(11\) | \(0\) | \(11\) | |||||
Minus space | \(-\) | \(172\) | \(53\) | \(119\) | \(160\) | \(53\) | \(107\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2325))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2325))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2325)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(775))\)\(^{\oplus 2}\)