# Properties

 Label 2.0.8.1-648.3-a Base field $$\Q(\sqrt{-2})$$ Weight $2$ Level norm $648$ Level $$\left(18 a\right)$$ Dimension $1$ CM no Base change yes Sign $-1$ Analytic rank odd

# Related objects

## Base field: $$\Q(\sqrt{-2})$$

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

## Form

 Weight: 2 Level: 648.3 = $$\left(18 a\right)$$ Level norm: 648 Dimension: 1 CM: no Base change: yes 72.2.a.a , 576.2.a.b Newspace: 2.0.8.1-648.3 (dimension 1) Sign of functional equation: $-1$ Analytic rank: odd

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$1$$
$$3$$ 3.1 = ($$-a - 1$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$-1$$

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$11$$ 11.1 = ($$a + 3$$) $$-4$$
$$11$$ 11.2 = ($$a - 3$$) $$-4$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-2$$
$$17$$ 17.2 = ($$2 a + 3$$) $$-2$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$-4$$
$$19$$ 19.2 = ($$3 a + 1$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$6$$
$$41$$ 41.2 = ($$4 a - 3$$) $$6$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$4$$
$$43$$ 43.2 = ($$3 a - 5$$) $$4$$
$$49$$ 49.1 = ($$7$$) $$-14$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$-4$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$-4$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$-4$$
$$67$$ 67.2 = ($$3 a + 7$$) $$-4$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$10$$
$$73$$ 73.2 = ($$6 a + 1$$) $$10$$
$$83$$ 83.1 = ($$a + 9$$) $$4$$
$$83$$ 83.2 = ($$a - 9$$) $$4$$
 Display number of eigenvalues