Defining parameters
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(1488\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6039))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 752 | 250 | 502 |
Cusp forms | 737 | 250 | 487 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | \(61\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(25\) |
\(+\) | \(+\) | \(-\) | $-$ | \(25\) |
\(+\) | \(-\) | \(+\) | $-$ | \(25\) |
\(+\) | \(-\) | \(-\) | $+$ | \(25\) |
\(-\) | \(+\) | \(+\) | $-$ | \(44\) |
\(-\) | \(+\) | \(-\) | $+$ | \(29\) |
\(-\) | \(-\) | \(+\) | $+$ | \(31\) |
\(-\) | \(-\) | \(-\) | $-$ | \(46\) |
Plus space | \(+\) | \(110\) | ||
Minus space | \(-\) | \(140\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6039))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6039)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(549))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2013))\)\(^{\oplus 2}\)