Defining parameters
Level: | \( N \) | \(=\) | \( 4761 = 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4761.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 50 \) | ||
Sturm bound: | \(1104\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4761))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 600 | 221 | 379 |
Cusp forms | 505 | 200 | 305 |
Eisenstein series | 95 | 21 | 74 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(144\) | \(36\) | \(108\) | \(121\) | \(36\) | \(85\) | \(23\) | \(0\) | \(23\) | |||
\(+\) | \(-\) | \(-\) | \(156\) | \(48\) | \(108\) | \(132\) | \(48\) | \(84\) | \(24\) | \(0\) | \(24\) | |||
\(-\) | \(+\) | \(-\) | \(156\) | \(71\) | \(85\) | \(132\) | \(61\) | \(71\) | \(24\) | \(10\) | \(14\) | |||
\(-\) | \(-\) | \(+\) | \(144\) | \(66\) | \(78\) | \(120\) | \(55\) | \(65\) | \(24\) | \(11\) | \(13\) | |||
Plus space | \(+\) | \(288\) | \(102\) | \(186\) | \(241\) | \(91\) | \(150\) | \(47\) | \(11\) | \(36\) | ||||
Minus space | \(-\) | \(312\) | \(119\) | \(193\) | \(264\) | \(109\) | \(155\) | \(48\) | \(10\) | \(38\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4761))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4761))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4761)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)