# Properties

 Base field $$\Q(\sqrt{-11})$$ Weight 2 Level norm 1584 Level $$\left(-24 a + 12\right)$$ Label 2.0.11.1-1584.2-b 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 1584.2 = $$\left(-24 a + 12\right)$$ Label 2.0.11.1-1584.2-b Dimension: 1 CM: no Base change: yes 132.2.a.b , 1452.2.a.f Newspace: 2.0.11.1-1584.2 (dimension 2) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 630

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$
$$3$$ 3.1 = ($$-a$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$1$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$-1$$

## 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 we only show 50. 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 = ($$-a - 1$$) $$2$$
$$5$$ 5.2 = ($$a - 2$$) $$2$$
$$23$$ 23.1 = ($$a + 4$$) $$0$$
$$23$$ 23.2 = ($$a - 5$$) $$0$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$-8$$
$$31$$ 31.2 = ($$3 a + 1$$) $$-8$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$10$$
$$37$$ 37.2 = ($$3 a - 5$$) $$10$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$-8$$
$$47$$ 47.2 = ($$2 a + 5$$) $$-8$$
$$49$$ 49.1 = ($$7$$) $$-10$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$-2$$
$$53$$ 53.2 = ($$4 a + 1$$) $$-2$$
$$59$$ 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 = ($$-5 a + 1$$) $$8$$
$$71$$ 71.2 = ($$5 a - 4$$) $$8$$
$$89$$ 89.1 = ($$5 a + 2$$) $$-14$$
$$89$$ 89.2 = ($$5 a - 7$$) $$-14$$
$$97$$ 97.1 = ($$-3 a + 10$$) $$-2$$
$$97$$ 97.2 = ($$3 a + 7$$) $$-2$$
$$103$$ 103.1 = ($$-6 a + 1$$) $$4$$
$$103$$ 103.2 = ($$6 a - 5$$) $$4$$
$$113$$ 113.1 = ($$a + 10$$) $$6$$
$$113$$ 113.2 = ($$a - 11$$) $$6$$
$$137$$ 137.1 = ($$7 a - 5$$) $$-2$$
$$137$$ 137.2 = ($$7 a - 2$$) $$-2$$
$$157$$ 157.1 = ($$-3 a + 13$$) $$6$$
$$157$$ 157.2 = ($$3 a + 10$$) $$6$$
$$163$$ 163.1 = ($$-6 a - 5$$) $$16$$
$$163$$ 163.2 = ($$6 a - 11$$) $$16$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$-5 a + 13$$) $$-12$$
$$179$$ 179.2 = ($$-5 a - 8$$) $$-12$$
$$181$$ 181.1 = ($$-3 a - 11$$) $$-10$$
$$181$$ 181.2 = ($$3 a - 14$$) $$-10$$
$$191$$ 191.1 = ($$-7 a + 11$$) $$16$$
$$191$$ 191.2 = ($$-7 a - 4$$) $$16$$
$$199$$ 199.1 = ($$-6 a + 13$$) $$-16$$
$$199$$ 199.2 = ($$6 a + 7$$) $$-16$$
$$223$$ 223.1 = ($$-9 a + 5$$) $$-4$$
$$223$$ 223.2 = ($$-9 a + 4$$) $$-4$$
$$229$$ 229.1 = ($$9 a - 7$$) $$-14$$
$$229$$ 229.2 = ($$9 a - 2$$) $$-14$$
$$251$$ 251.1 = ($$-5 a + 16$$) $$4$$
$$251$$ 251.2 = ($$5 a + 11$$) $$4$$
$$257$$ 257.1 = ($$-8 a - 5$$) $$-30$$
$$257$$ 257.2 = ($$-8 a + 13$$) $$-30$$