Defining parameters
Level: | \( N \) | \(=\) | \( 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 31.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(5\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(31))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3 | 3 | 0 |
Cusp forms | 2 | 2 | 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.
\(31\) | Dim |
---|---|
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 31 | |||||||
31.2.a.a | $2$ | $0.248$ | \(\Q(\sqrt{5}) \) | None | \(1\) | \(-2\) | \(2\) | \(-4\) | $-$ | \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\) |