Defining parameters
Level: | \( N \) | \(=\) | \( 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 859.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(143\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(859))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 72 | 0 |
Cusp forms | 71 | 71 | 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.
\(859\) | Dim |
---|---|
\(+\) | \(29\) |
\(-\) | \(42\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(859))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 859 | |||||||
859.2.a.a | $29$ | $6.859$ | None | \(-10\) | \(-5\) | \(-21\) | \(-4\) | $+$ | |||
859.2.a.b | $42$ | $6.859$ | None | \(10\) | \(1\) | \(21\) | \(2\) | $-$ |