# Properties

 Base field $$\Q(\sqrt{-2})$$ Weight 2 Level norm 578 Level $$\left(17 a\right)$$ Label 2.0.8.1-578.2-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Related objects

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

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

## Form

 Weight 2 Level 578.2 = $$\left(17 a\right)$$ Label 2.0.8.1-578.2-a Dimension: 1 CM: no Base change: yes 34.2.a.a , 1088.2.a.d Newspace: 2.0.8.1-578.2 (dimension 1) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 1

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$1$$
$$3$$ 3.1 = ($$-a - 1$$) $$-2$$
$$3$$ 3.2 = ($$a - 1$$) $$-2$$
$$11$$ 11.1 = ($$a + 3$$) $$6$$
$$11$$ 11.2 = ($$a - 3$$) $$6$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-1$$
$$17$$ 17.2 = ($$2 a + 3$$) $$-1$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$-4$$
$$19$$ 19.2 = ($$3 a + 1$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$-10$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$6$$
$$41$$ 41.2 = ($$4 a - 3$$) $$6$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$8$$
$$43$$ 43.2 = ($$3 a - 5$$) $$8$$
$$49$$ 49.1 = ($$7$$) $$2$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$0$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$0$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$8$$
$$67$$ 67.2 = ($$3 a + 7$$) $$8$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$2$$
$$73$$ 73.2 = ($$6 a + 1$$) $$2$$
$$83$$ 83.1 = ($$a + 9$$) $$0$$
$$83$$ 83.2 = ($$a - 9$$) $$0$$
$$89$$ 89.1 = ($$-2 a + 9$$) $$-6$$
$$89$$ 89.2 = ($$2 a + 9$$) $$-6$$
$$97$$ 97.1 = ($$-6 a - 5$$) $$14$$
$$97$$ 97.2 = ($$6 a - 5$$) $$14$$
$$107$$ 107.1 = ($$7 a + 3$$) $$-6$$
$$107$$ 107.2 = ($$7 a - 3$$) $$-6$$
$$113$$ 113.1 = ($$-4 a + 9$$) $$-6$$
$$113$$ 113.2 = ($$4 a + 9$$) $$-6$$
$$131$$ 131.1 = ($$-5 a - 9$$) $$-6$$
$$131$$ 131.2 = ($$5 a - 9$$) $$-6$$
$$137$$ 137.1 = ($$-8 a + 3$$) $$6$$
$$137$$ 137.2 = ($$-8 a - 3$$) $$6$$
$$139$$ 139.1 = ($$-3 a - 11$$) $$2$$
$$139$$ 139.2 = ($$3 a - 11$$) $$2$$
$$163$$ 163.1 = ($$-9 a + 1$$) $$2$$
$$163$$ 163.2 = ($$9 a + 1$$) $$2$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$7 a + 9$$) $$12$$
$$179$$ 179.2 = ($$7 a - 9$$) $$12$$
$$193$$ 193.1 = ($$-6 a - 11$$) $$-10$$
$$193$$ 193.2 = ($$6 a - 11$$) $$-10$$
$$211$$ 211.1 = ($$9 a - 7$$) $$-10$$
$$211$$ 211.2 = ($$9 a + 7$$) $$-10$$
$$227$$ 227.1 = ($$a + 15$$) $$-6$$
$$227$$ 227.2 = ($$a - 15$$) $$-6$$
$$233$$ 233.1 = ($$-2 a + 15$$) $$18$$
$$233$$ 233.2 = ($$2 a + 15$$) $$18$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$1$$
$$17$$ 17.2 = ($$2 a + 3$$) $$1$$