# Properties

 Base field $$\Q(\sqrt{-2})$$ Weight 2 Level norm 10082 Level $$\left(71 a\right)$$ Label 2.0.8.1-10082.1-e 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 10082.1 = $$\left(71 a\right)$$ Label 2.0.8.1-10082.1-e Dimension: 1 CM: no Base change: yes 4544.2.a.k , 142.2.a.e Newspace: 2.0.8.1-10082.1 (dimension 5) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$1$$
$$3$$ 3.1 = ($$-a - 1$$) $$1$$
$$3$$ 3.2 = ($$a - 1$$) $$1$$
$$11$$ 11.1 = ($$a + 3$$) $$0$$
$$11$$ 11.2 = ($$a - 3$$) $$0$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$0$$
$$17$$ 17.2 = ($$2 a + 3$$) $$0$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$-1$$
$$19$$ 19.2 = ($$3 a + 1$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-10$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$0$$
$$41$$ 41.2 = ($$4 a - 3$$) $$0$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$-1$$
$$43$$ 43.2 = ($$3 a - 5$$) $$-1$$
$$49$$ 49.1 = ($$7$$) $$-13$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$6$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$6$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$8$$
$$67$$ 67.2 = ($$3 a + 7$$) $$8$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$-1$$
$$73$$ 73.2 = ($$6 a + 1$$) $$-1$$
$$83$$ 83.1 = ($$a + 9$$) $$12$$
$$83$$ 83.2 = ($$a - 9$$) $$12$$
$$89$$ 89.1 = ($$-2 a + 9$$) $$-3$$
$$89$$ 89.2 = ($$2 a + 9$$) $$-3$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$5041$$ 5041.1 = ($$71$$) $$-1$$