Defining parameters
Level: | \( N \) | \(=\) | \( 6137 = 17 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6137.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 23 \) | ||
Sturm bound: | \(1140\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6137))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 590 | 454 | 136 |
Cusp forms | 551 | 454 | 97 |
Eisenstein series | 39 | 0 | 39 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(17\) | \(19\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(103\) |
\(+\) | \(-\) | $-$ | \(123\) |
\(-\) | \(+\) | $-$ | \(123\) |
\(-\) | \(-\) | $+$ | \(105\) |
Plus space | \(+\) | \(208\) | |
Minus space | \(-\) | \(246\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6137))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6137))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6137)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(323))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)