Bianchi cusp form 39204.15-a over Q(−2)\Q(\sqrt{-2})

• Label: 2.0.8.1-39204.15-a
• Base field: $\Q(\sqrt{-2})$
• Weight: $2$
• Level norm: $39204$
• Level: $\left(-140 a + 2\right)$
• Dimension: $1$
• CM: no
• Base change: no
• Sign: $-1$
• Analytic rank: odd

Base field: $\Q(\sqrt{-2})$

Generator $a$, with minimal polynomial $x^2 + 2$; class number $1$.

Form

Weight:	2
Level:	39204.15 = $\left(-140 a + 2\right)$
Level norm:	39204
Dimension:	1
CM:	no
Base change:	no
Newspace:	2.0.8.1-39204.15 (dimension 8)
Sign of functional equation:	$-1$
Analytic rank:	odd

Associated elliptic curves

This Bianchi newform is associated to the isogeny class 2.0.8.1-39204.15-a of elliptic curves.

Atkin-Lehner eigenvalues

Norm	Prime	Eigenvalue
$2$	2.1 = $\left(a\right)$	$-1$
$3$	3.2 = $\left(a - 1\right)$	$1$
$11$	11.2 = $\left(a - 3\right)$	$-1$

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$	$\mathfrak{p}$	$a_{\mathfrak{p}}$
$3$	3.1 = $\left(-a - 1\right)$	$-2$
$11$	11.1 = $\left(a + 3\right)$	$0$
$17$	17.1 = $\left(-2 a + 3\right)$	$3$
$17$	17.2 = $\left(2 a + 3\right)$	$6$
$19$	19.1 = $\left(-3 a + 1\right)$	$2$
$19$	19.2 = $\left(3 a + 1\right)$	$-4$
$25$	25.1 = $\left(5\right)$	$-1$
$41$	41.1 = $\left(-4 a - 3\right)$	$-9$
$41$	41.2 = $\left(4 a - 3\right)$	$3$
$43$	43.1 = $\left(-3 a - 5\right)$	$2$
$43$	43.2 = $\left(3 a - 5\right)$	$8$
$49$	49.1 = $\left(7\right)$	$-1$
$59$	59.1 = $\left(-5 a + 3\right)$	$-6$
$59$	59.2 = $\left(-5 a - 3\right)$	$-6$
$67$	67.1 = $\left(-3 a + 7\right)$	$14$
$67$	67.2 = $\left(3 a + 7\right)$	$-10$
$73$	73.1 = $\left(-6 a + 1\right)$	$11$
$73$	73.2 = $\left(6 a + 1\right)$	$14$
$83$	83.1 = $\left(a + 9\right)$	$-6$
$83$	83.2 = $\left(a - 9\right)$	$6$

Display number of eigenvalues