Defining parameters
Level: | \( N \) | \(=\) | \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9405.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 48 \) | ||
Sturm bound: | \(2880\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9405))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1456 | 300 | 1156 |
Cusp forms | 1425 | 300 | 1125 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(11\) | \(19\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(15\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(19\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(15\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(11\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(15\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(11\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(15\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(19\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(23\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(21\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(23\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(25\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(22\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(24\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(22\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(20\) |
Plus space | \(+\) | \(138\) | |||
Minus space | \(-\) | \(162\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9405))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9405))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9405)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1881))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3135))\)\(^{\oplus 2}\)