# Properties

 Label 2.0.8.1-38416.1-b Base field $$\Q(\sqrt{-2})$$ Weight $2$ Level norm $38416$ Level $$\left(196\right)$$ 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: 38416.1 = $$\left(196\right)$$ Level norm: 38416 Dimension: 1 CM: no Base change: yes 784.2.a.b , 3136.2.a.e Newspace: 2.0.8.1-38416.1 (dimension 42) Sign of functional equation: $-1$ Analytic rank: odd

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = $$\left(a\right)$$ $$1$$
$$49$$ 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 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$3$$ 3.1 = $$\left(-a - 1\right)$$ $$-2$$
$$3$$ 3.2 = $$\left(a - 1\right)$$ $$-2$$
$$11$$ 11.1 = $$\left(a + 3\right)$$ $$0$$
$$11$$ 11.2 = $$\left(a - 3\right)$$ $$0$$
$$17$$ 17.1 = $$\left(-2 a + 3\right)$$ $$-6$$
$$17$$ 17.2 = $$\left(2 a + 3\right)$$ $$-6$$
$$19$$ 19.1 = $$\left(-3 a + 1\right)$$ $$2$$
$$19$$ 19.2 = $$\left(3 a + 1\right)$$ $$2$$
$$25$$ 25.1 = $$\left(5\right)$$ $$-10$$
$$41$$ 41.1 = $$\left(-4 a - 3\right)$$ $$-6$$
$$41$$ 41.2 = $$\left(4 a - 3\right)$$ $$-6$$
$$43$$ 43.1 = $$\left(-3 a - 5\right)$$ $$-8$$
$$43$$ 43.2 = $$\left(3 a - 5\right)$$ $$-8$$
$$59$$ 59.1 = $$\left(-5 a + 3\right)$$ $$-6$$
$$59$$ 59.2 = $$\left(-5 a - 3\right)$$ $$-6$$
$$67$$ 67.1 = $$\left(-3 a + 7\right)$$ $$4$$
$$67$$ 67.2 = $$\left(3 a + 7\right)$$ $$4$$
$$73$$ 73.1 = $$\left(-6 a + 1\right)$$ $$-2$$
$$73$$ 73.2 = $$\left(6 a + 1\right)$$ $$-2$$
$$83$$ 83.1 = $$\left(a + 9\right)$$ $$-6$$
 Display number of eigenvalues