# Properties

 Base field $$\Q(\sqrt{-2})$$ Weight 2 Level norm 6822 Level $$\left(57 a - 18\right)$$ Label 2.0.8.1-6822.4-b Dimension 1 CM no Base-change no 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 6822.4 = $$\left(57 a - 18\right)$$ Label 2.0.8.1-6822.4-b Dimension: 1 CM: no Base change: no Newspace: 2.0.8.1-6822.4 (dimension 3) 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 = ($$a - 1$$) $$-1$$
$$379$$ 379.2 = ($$3 a + 19$$) $$1$$

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$11$$ 11.1 = ($$a + 3$$) $$-2$$
$$11$$ 11.2 = ($$a - 3$$) $$-3$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-3$$
$$17$$ 17.2 = ($$2 a + 3$$) $$4$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$-2$$
$$19$$ 19.2 = ($$3 a + 1$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$-8$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$-2$$
$$41$$ 41.2 = ($$4 a - 3$$) $$4$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$4$$
$$43$$ 43.2 = ($$3 a - 5$$) $$9$$
$$49$$ 49.1 = ($$7$$) $$-10$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$-12$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$11$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$5$$
$$67$$ 67.2 = ($$3 a + 7$$) $$7$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$6$$
$$73$$ 73.2 = ($$6 a + 1$$) $$-7$$
$$83$$ 83.1 = ($$a + 9$$) $$-9$$
$$83$$ 83.2 = ($$a - 9$$) $$-3$$
$$89$$ 89.1 = ($$-2 a + 9$$) $$-15$$
$$89$$ 89.2 = ($$2 a + 9$$) $$8$$
$$97$$ 97.1 = ($$-6 a - 5$$) $$-10$$
$$97$$ 97.2 = ($$6 a - 5$$) $$-8$$
$$107$$ 107.1 = ($$7 a + 3$$) $$6$$
$$107$$ 107.2 = ($$7 a - 3$$) $$-12$$
$$113$$ 113.1 = ($$-4 a + 9$$) $$-1$$
$$113$$ 113.2 = ($$4 a + 9$$) $$6$$
$$131$$ 131.1 = ($$-5 a - 9$$) $$0$$
$$131$$ 131.2 = ($$5 a - 9$$) $$-3$$
$$137$$ 137.1 = ($$-8 a + 3$$) $$-20$$
$$137$$ 137.2 = ($$-8 a - 3$$) $$-8$$
$$139$$ 139.1 = ($$-3 a - 11$$) $$-16$$
$$139$$ 139.2 = ($$3 a - 11$$) $$16$$
$$163$$ 163.1 = ($$-9 a + 1$$) $$-8$$
$$163$$ 163.2 = ($$9 a + 1$$) $$5$$
$$169$$ 169.1 = ($$13$$) $$-19$$
$$179$$ 179.1 = ($$7 a + 9$$) $$-16$$
$$179$$ 179.2 = ($$7 a - 9$$) $$19$$
$$193$$ 193.1 = ($$-6 a - 11$$) $$-12$$
$$193$$ 193.2 = ($$6 a - 11$$) $$-4$$
$$211$$ 211.1 = ($$9 a - 7$$) $$-17$$
$$211$$ 211.2 = ($$9 a + 7$$) $$3$$
$$227$$ 227.1 = ($$a + 15$$) $$-12$$
$$227$$ 227.2 = ($$a - 15$$) $$17$$
$$233$$ 233.1 = ($$-2 a + 15$$) $$10$$
$$233$$ 233.2 = ($$2 a + 15$$) $$-6$$
$$241$$ 241.1 = ($$-6 a + 13$$) $$-27$$
$$241$$ 241.2 = ($$6 a + 13$$) $$-26$$
$$251$$ 251.1 = ($$-11 a + 3$$) $$-14$$
$$251$$ 251.2 = ($$-11 a - 3$$) $$-6$$