# Properties

 Base field $$\Q(\sqrt{-2})$$ Weight 2 Level norm 15138 Level $$\left(87 a\right)$$ Label 2.0.8.1-15138.2-g Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Learn more about

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

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

## Form

 Weight 2 Level 15138.2 = $$\left(87 a\right)$$ Label 2.0.8.1-15138.2-g Dimension: 1 CM: no Base change: yes 5568.2.a.bc , 174.2.a.e Newspace: 2.0.8.1-15138.2 (dimension 7) 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 = ($$a + 3$$) $$-2$$
$$11$$ 11.2 = ($$a - 3$$) $$-2$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-3$$
$$17$$ 17.2 = ($$2 a + 3$$) $$-3$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$-1$$
$$19$$ 19.2 = ($$3 a + 1$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-9$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$-7$$
$$41$$ 41.2 = ($$4 a - 3$$) $$-7$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$9$$
$$43$$ 43.2 = ($$3 a - 5$$) $$9$$
$$49$$ 49.1 = ($$7$$) $$-13$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$-3$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$-3$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$12$$
$$67$$ 67.2 = ($$3 a + 7$$) $$12$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$-10$$
$$73$$ 73.2 = ($$6 a + 1$$) $$-10$$
$$83$$ 83.1 = ($$a + 9$$) $$0$$
$$83$$ 83.2 = ($$a - 9$$) $$0$$
$$89$$ 89.1 = ($$-2 a + 9$$) $$6$$
$$89$$ 89.2 = ($$2 a + 9$$) $$6$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$3$$ 3.1 = ($$-a - 1$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$-1$$
$$841$$ 841.1 = ($$29$$) $$-1$$