Defining parameters
Level: | \( N \) | \(=\) | \( 6171 = 3 \cdot 11^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6171.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 45 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6171))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 816 | 290 | 526 |
Cusp forms | 769 | 290 | 479 |
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.
\(3\) | \(11\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(34\) |
\(+\) | \(+\) | \(-\) | $-$ | \(42\) |
\(+\) | \(-\) | \(+\) | $-$ | \(40\) |
\(+\) | \(-\) | \(-\) | $+$ | \(30\) |
\(-\) | \(+\) | \(+\) | $-$ | \(38\) |
\(-\) | \(+\) | \(-\) | $+$ | \(30\) |
\(-\) | \(-\) | \(+\) | $+$ | \(33\) |
\(-\) | \(-\) | \(-\) | $-$ | \(43\) |
Plus space | \(+\) | \(127\) | ||
Minus space | \(-\) | \(163\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6171))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6171))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6171)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2057))\)\(^{\oplus 2}\)