Defining parameters
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 76 \) | ||
Sturm bound: | \(3600\) | ||
Trace bound: | \(23\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(23\), \(53\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8550))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1848 | 143 | 1705 |
Cusp forms | 1753 | 143 | 1610 |
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.
\(2\) | \(3\) | \(5\) | \(19\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(105\) | \(7\) | \(98\) | \(100\) | \(7\) | \(93\) | \(5\) | \(0\) | \(5\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(123\) | \(6\) | \(117\) | \(117\) | \(6\) | \(111\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(123\) | \(7\) | \(116\) | \(117\) | \(7\) | \(110\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(111\) | \(9\) | \(102\) | \(105\) | \(9\) | \(96\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(120\) | \(12\) | \(108\) | \(114\) | \(12\) | \(102\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(111\) | \(8\) | \(103\) | \(105\) | \(8\) | \(97\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(114\) | \(10\) | \(104\) | \(108\) | \(10\) | \(98\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(117\) | \(12\) | \(105\) | \(111\) | \(12\) | \(99\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(117\) | \(7\) | \(110\) | \(111\) | \(7\) | \(104\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(117\) | \(6\) | \(111\) | \(111\) | \(6\) | \(105\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(111\) | \(7\) | \(104\) | \(105\) | \(7\) | \(98\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(117\) | \(9\) | \(108\) | \(111\) | \(9\) | \(102\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(120\) | \(8\) | \(112\) | \(114\) | \(8\) | \(106\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(111\) | \(13\) | \(98\) | \(105\) | \(13\) | \(92\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(114\) | \(13\) | \(101\) | \(108\) | \(13\) | \(95\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(117\) | \(9\) | \(108\) | \(111\) | \(9\) | \(102\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(906\) | \(64\) | \(842\) | \(859\) | \(64\) | \(795\) | \(47\) | \(0\) | \(47\) | ||||||
Minus space | \(-\) | \(942\) | \(79\) | \(863\) | \(894\) | \(79\) | \(815\) | \(48\) | \(0\) | \(48\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8550))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8550)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1710))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\)\(^{\oplus 2}\)