Defining parameters
Level: | \( N \) | \(=\) | \( 9675 = 3^{2} \cdot 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9675.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 80 \) | ||
Sturm bound: | \(2640\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9675))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1344 | 332 | 1012 |
Cusp forms | 1297 | 332 | 965 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(43\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(26\) |
\(+\) | \(+\) | \(-\) | $-$ | \(38\) |
\(+\) | \(-\) | \(+\) | $-$ | \(38\) |
\(+\) | \(-\) | \(-\) | $+$ | \(30\) |
\(-\) | \(+\) | \(+\) | $-$ | \(50\) |
\(-\) | \(+\) | \(-\) | $+$ | \(44\) |
\(-\) | \(-\) | \(+\) | $+$ | \(51\) |
\(-\) | \(-\) | \(-\) | $-$ | \(55\) |
Plus space | \(+\) | \(151\) | ||
Minus space | \(-\) | \(181\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9675))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9675))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(645))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1075))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1935))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3225))\)\(^{\oplus 2}\)