# Properties

 Label 2.0.11.1-16731.2-b Base field $$\Q(\sqrt{-11})$$ Weight $2$ Level norm $16731$ Level $$\left(-78 a + 39\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$\ge2$$, even

# Related objects

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

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

## Form

 Weight: 2 Level: 16731.2 = $$\left(-78 a + 39\right)$$ Level norm: 16731 Dimension: 1 CM: no Base change: yes 4719.2.a.k , 429.2.a.b Newspace: 2.0.11.1-16731.2 (dimension 19) Sign of functional equation: $+1$ Analytic rank: $$\ge2$$, even

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$-1$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$1$$
$$169$$ 169.1 = ($$13$$) $$-1$$

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$4$$ 4.1 = ($$2$$) $$-3$$
$$5$$ 5.1 = ($$-a - 1$$) $$-2$$
$$5$$ 5.2 = ($$a - 2$$) $$-2$$
$$23$$ 23.1 = ($$a + 4$$) $$-8$$
$$23$$ 23.2 = ($$a - 5$$) $$-8$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$0$$
$$31$$ 31.2 = ($$3 a + 1$$) $$0$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$6$$
$$37$$ 37.2 = ($$3 a - 5$$) $$6$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$8$$
$$47$$ 47.2 = ($$2 a + 5$$) $$8$$
$$49$$ 49.1 = ($$7$$) $$-14$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$-10$$
$$53$$ 53.2 = ($$4 a + 1$$) $$-10$$
$$59$$ 59.1 = ($$a + 7$$) $$-12$$
$$59$$ 59.2 = ($$a - 8$$) $$-12$$
$$67$$ 67.1 = ($$-3 a - 5$$) $$-12$$
$$67$$ 67.2 = ($$3 a - 8$$) $$-12$$
$$71$$ 71.1 = ($$-5 a + 1$$) $$0$$
$$71$$ 71.2 = ($$5 a - 4$$) $$0$$
$$89$$ 89.1 = ($$5 a + 2$$) $$2$$
 Display number of eigenvalues