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 | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(7\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(6\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(7\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(12\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(8\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(10\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(12\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(7\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(7\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(9\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(8\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(13\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(13\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(9\) |
Plus space | \(+\) | \(64\) | |||
Minus space | \(-\) | \(79\) |
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
\( S_{2}^{\mathrm{old}}(\Gamma_0(8550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1710))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\)\(^{\oplus 2}\)