Defining parameters
Level: | \( N \) | \(=\) | \( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6498.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 59 \) | ||
Sturm bound: | \(2280\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(13\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6498))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1220 | 143 | 1077 |
Cusp forms | 1061 | 143 | 918 |
Eisenstein series | 159 | 0 | 159 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(17\) |
\(+\) | \(+\) | \(-\) | $-$ | \(12\) |
\(+\) | \(-\) | \(+\) | $-$ | \(22\) |
\(+\) | \(-\) | \(-\) | $+$ | \(20\) |
\(-\) | \(+\) | \(+\) | $-$ | \(17\) |
\(-\) | \(+\) | \(-\) | $+$ | \(12\) |
\(-\) | \(-\) | \(+\) | $+$ | \(18\) |
\(-\) | \(-\) | \(-\) | $-$ | \(25\) |
Plus space | \(+\) | \(67\) | ||
Minus space | \(-\) | \(76\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6498))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6498)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3249))\)\(^{\oplus 2}\)