Defining parameters
Level: | \( N \) | \(=\) | \( 9386 = 2 \cdot 13 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9386.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 56 \) | ||
Sturm bound: | \(2660\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9386))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1370 | 341 | 1029 |
Cusp forms | 1291 | 341 | 950 |
Eisenstein series | 79 | 0 | 79 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(13\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(39\) |
\(+\) | \(+\) | \(-\) | $-$ | \(45\) |
\(+\) | \(-\) | \(+\) | $-$ | \(50\) |
\(+\) | \(-\) | \(-\) | $+$ | \(36\) |
\(-\) | \(+\) | \(+\) | $-$ | \(50\) |
\(-\) | \(+\) | \(-\) | $+$ | \(36\) |
\(-\) | \(-\) | \(+\) | $+$ | \(31\) |
\(-\) | \(-\) | \(-\) | $-$ | \(54\) |
Plus space | \(+\) | \(142\) | ||
Minus space | \(-\) | \(199\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9386))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9386))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9386)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(494))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4693))\)\(^{\oplus 2}\)