Defining parameters
Level: | \( N \) | \(=\) | \( 7935 = 3 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7935.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 49 \) | ||
Sturm bound: | \(2208\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7935))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1152 | 336 | 816 |
Cusp forms | 1057 | 336 | 721 |
Eisenstein series | 95 | 0 | 95 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(132\) | \(41\) | \(91\) | \(121\) | \(41\) | \(80\) | \(11\) | \(0\) | \(11\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(154\) | \(44\) | \(110\) | \(142\) | \(44\) | \(98\) | \(12\) | \(0\) | \(12\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(156\) | \(51\) | \(105\) | \(144\) | \(51\) | \(93\) | \(12\) | \(0\) | \(12\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(134\) | \(33\) | \(101\) | \(122\) | \(33\) | \(89\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(144\) | \(43\) | \(101\) | \(132\) | \(43\) | \(89\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(144\) | \(40\) | \(104\) | \(132\) | \(40\) | \(92\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(144\) | \(33\) | \(111\) | \(132\) | \(33\) | \(99\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(144\) | \(51\) | \(93\) | \(132\) | \(51\) | \(81\) | \(12\) | \(0\) | \(12\) | |||
Plus space | \(+\) | \(554\) | \(147\) | \(407\) | \(507\) | \(147\) | \(360\) | \(47\) | \(0\) | \(47\) | |||||
Minus space | \(-\) | \(598\) | \(189\) | \(409\) | \(550\) | \(189\) | \(361\) | \(48\) | \(0\) | \(48\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7935))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7935)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\)\(^{\oplus 2}\)