# Properties

 Label 2.0.11.1-539.1-b Base field $$\Q(\sqrt{-11})$$ Weight $2$ Level norm $539$ Level $$\left(-14 a + 7\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$0$$

# Related objects

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

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

## Form

 Weight: 2 Level: 539.1 = $$\left(-14 a + 7\right)$$ Level norm: 539 Dimension: 1 CM: no Base change: yes 847.2.a.c , 77.2.a.b Newspace: 2.0.11.1-539.1 (dimension 5) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 64

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$11$$ 11.1 = $$\left(-2 a + 1\right)$$ $$1$$
$$49$$ 49.1 = $$\left(7\right)$$ $$-1$$

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 1000 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 = $$\left(-a\right)$$ $$1$$
$$3$$ 3.2 = $$\left(a - 1\right)$$ $$1$$
$$4$$ 4.1 = $$\left(2\right)$$ $$-4$$
$$5$$ 5.1 = $$\left(-a - 1\right)$$ $$3$$
$$5$$ 5.2 = $$\left(a - 2\right)$$ $$3$$
$$23$$ 23.1 = $$\left(a + 4\right)$$ $$3$$
$$23$$ 23.2 = $$\left(a - 5\right)$$ $$3$$
$$31$$ 31.1 = $$\left(-3 a + 4\right)$$ $$5$$
$$31$$ 31.2 = $$\left(3 a + 1\right)$$ $$5$$
$$37$$ 37.1 = $$\left(-3 a - 2\right)$$ $$11$$
$$37$$ 37.2 = $$\left(3 a - 5\right)$$ $$11$$
$$47$$ 47.1 = $$\left(-2 a + 7\right)$$ $$0$$
$$47$$ 47.2 = $$\left(2 a + 5\right)$$ $$0$$
$$53$$ 53.1 = $$\left(-4 a + 5\right)$$ $$-6$$
$$53$$ 53.2 = $$\left(4 a + 1\right)$$ $$-6$$
$$59$$ 59.1 = $$\left(a + 7\right)$$ $$-9$$
$$59$$ 59.2 = $$\left(a - 8\right)$$ $$-9$$
$$67$$ 67.1 = $$\left(-3 a - 5\right)$$ $$5$$
$$67$$ 67.2 = $$\left(3 a - 8\right)$$ $$5$$
$$71$$ 71.1 = $$\left(-5 a + 1\right)$$ $$9$$
 Display number of eigenvalues