Bianchi cusp form 9984.1-b over Q(−3)\Q(\sqrt{-3})

• Label: 2.0.3.1-9984.1-b
• Base field: $\Q(\sqrt{-3})$
• Weight: $2$
• Level norm: $9984$
• Level: $\left(-32 a + 112\right)$
• Dimension: $1$
• CM: no
• Base change: no
• Sign: $-1$
• Analytic rank: odd

Base field: $\Q(\sqrt{-3})$

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

Form

Weight:	2
Level:	9984.1 = $\left(-32 a + 112\right)$
Level norm:	9984
Dimension:	1
CM:	no
Base change:	no
Newspace:	2.0.3.1-9984.1 (dimension 3)
Sign of functional equation:	$-1$
Analytic rank:	odd

Associated elliptic curves

This Bianchi newform is associated to the isogeny class 2.0.3.1-9984.1-b of elliptic curves.

Atkin-Lehner eigenvalues

Norm	Prime	Eigenvalue
$3$	3.1 = $\left(a + 1\right)$	$1$
$4$	4.1 = $\left(2\right)$	$-1$
$13$	13.1 = $\left(a + 3\right)$	$-1$

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.

$N(\mathfrak{p})$	$\mathfrak{p}$	$a_{\mathfrak{p}}$
$7$	7.1 = $\left(-a - 2\right)$	$0$
$7$	7.2 = $\left(a - 3\right)$	$0$
$13$	13.2 = $\left(a - 4\right)$	$-2$
$19$	19.1 = $\left(-2 a + 5\right)$	$-4$
$19$	19.2 = $\left(2 a + 3\right)$	$-4$
$25$	25.1 = $\left(5\right)$	$2$
$31$	31.1 = $\left(a + 5\right)$	$-8$
$31$	31.2 = $\left(a - 6\right)$	$0$
$37$	37.1 = $\left(-3 a + 7\right)$	$-10$
$37$	37.2 = $\left(3 a + 4\right)$	$-2$
$43$	43.1 = $\left(a + 6\right)$	$4$
$43$	43.2 = $\left(a - 7\right)$	$-4$
$61$	61.1 = $\left(-4 a + 9\right)$	$6$
$61$	61.2 = $\left(4 a + 5\right)$	$6$
$67$	67.1 = $\left(-2 a + 9\right)$	$12$
$67$	67.2 = $\left(2 a + 7\right)$	$-12$
$73$	73.1 = $\left(a + 8\right)$	$2$
$73$	73.2 = $\left(a - 9\right)$	$-6$
$79$	79.1 = $\left(-3 a + 10\right)$	$8$
$79$	79.2 = $\left(3 a + 7\right)$	$8$

Display number of eigenvalues