Defining parameters
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(1008\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6047))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 505 | 505 | 0 |
Cusp forms | 504 | 504 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(6047\) | Dim |
---|---|
\(+\) | \(217\) |
\(-\) | \(287\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6047))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 6047 | |||||||
6047.2.a.a | $217$ | $48.286$ | None | \(-20\) | \(-27\) | \(-19\) | \(-48\) | $+$ | |||
6047.2.a.b | $287$ | $48.286$ | None | \(21\) | \(29\) | \(19\) | \(52\) | $-$ |