Bianchi cusp form 20736.4-f over Q(−11)\Q(\sqrt{-11})

• Label: 2.0.11.1-20736.4-f
• Base field: $\Q(\sqrt{-11})$
• Weight: $2$
• Level norm: $20736$
• Level: $\left(-48 a - 96\right)$
• Dimension: $1$
• CM: no
• Base change: no
• Sign: $-1$
• Analytic rank: odd

Base field: $\Q(\sqrt{-11})$

Generator $a$, with minimal polynomial $x^2 - x + 3$; class number $1$.

Form

Weight:	2
Level:	20736.4 = $\left(-48 a - 96\right)$
Level norm:	20736
Dimension:	1
CM:	no
Base change:	no
Newspace:	2.0.11.1-20736.4 (dimension 6)
Sign of functional equation:	$-1$
Analytic rank:	odd

Associated elliptic curves

This Bianchi newform is associated to the isogeny class 2.0.11.1-20736.4-f of elliptic curves.

Atkin-Lehner eigenvalues

Norm	Prime	Eigenvalue
$3$	3.1 = $\left(-a\right)$	$-1$
$3$	3.2 = $\left(a - 1\right)$	$1$
$4$	4.1 = $\left(2\right)$	$-1$

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.

$N(\mathfrak{p})$	$\mathfrak{p}$	$a_{\mathfrak{p}}$
$5$	5.1 = $\left(-a - 1\right)$	$1$
$5$	5.2 = $\left(a - 2\right)$	$-2$
$11$	11.1 = $\left(-2 a + 1\right)$	$3$
$23$	23.1 = $\left(a + 4\right)$	$-4$
$23$	23.2 = $\left(a - 5\right)$	$-2$
$31$	31.1 = $\left(-3 a + 4\right)$	$3$
$31$	31.2 = $\left(3 a + 1\right)$	$6$
$37$	37.1 = $\left(-3 a - 2\right)$	$-7$
$37$	37.2 = $\left(3 a - 5\right)$	$5$
$47$	47.1 = $\left(-2 a + 7\right)$	$4$
$47$	47.2 = $\left(2 a + 5\right)$	$-7$
$49$	49.1 = $\left(7\right)$	$-6$
$53$	53.1 = $\left(-4 a + 5\right)$	$-12$
$53$	53.2 = $\left(4 a + 1\right)$	$6$
$59$	59.1 = $\left(a + 7\right)$	$-9$
$59$	59.2 = $\left(a - 8\right)$	$-12$
$67$	67.1 = $\left(-3 a - 5\right)$	$0$
$67$	67.2 = $\left(3 a - 8\right)$	$3$
$71$	71.1 = $\left(-5 a + 1\right)$	$13$
$71$	71.2 = $\left(5 a - 4\right)$	$5$

Display number of eigenvalues