Defining parameters
Level: | \( N \) | \(=\) | \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5850.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 72 \) | ||
Sturm bound: | \(2520\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(17\), \(23\), \(31\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5850))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1308 | 95 | 1213 |
Cusp forms | 1213 | 95 | 1118 |
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.
\(2\) | \(3\) | \(5\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(4\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(5\) |
Plus space | \(+\) | \(43\) | |||
Minus space | \(-\) | \(52\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5850))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5850))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5850)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2925))\)\(^{\oplus 2}\)