Properties

 Base field $$\Q(\sqrt{-2})$$ Weight 2 Level norm 20449 Level $$\left(143\right)$$ Label 2.0.8.1-20449.2-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$\ge2$$, even

Related objects

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

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

Form

 Weight 2 Level 20449.2 = $$\left(143\right)$$ Label 2.0.8.1-20449.2-a Dimension: 1 CM: no Base change: yes 143.2.a.a , 9152.2.a.n Newspace: 2.0.8.1-20449.2 (dimension 11) Sign of functional equation: +1 Analytic rank: $$\ge2$$, even

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$0$$
$$3$$ 3.1 = ($$-a - 1$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$-1$$
$$11$$ 11.1 = ($$a + 3$$) $$-1$$
$$11$$ 11.2 = ($$a - 3$$) $$-1$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-4$$
$$17$$ 17.2 = ($$2 a + 3$$) $$-4$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$2$$
$$19$$ 19.2 = ($$3 a + 1$$) $$2$$
$$25$$ 25.1 = ($$5$$) $$-9$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$10$$
$$41$$ 41.2 = ($$4 a - 3$$) $$10$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$-4$$
$$43$$ 43.2 = ($$3 a - 5$$) $$-4$$
$$49$$ 49.1 = ($$7$$) $$-10$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$-1$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$-1$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$-1$$
$$67$$ 67.2 = ($$3 a + 7$$) $$-1$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$-16$$
$$73$$ 73.2 = ($$6 a + 1$$) $$-16$$
$$83$$ 83.1 = ($$a + 9$$) $$0$$
$$83$$ 83.2 = ($$a - 9$$) $$0$$
$$89$$ 89.1 = ($$-2 a + 9$$) $$-7$$
$$89$$ 89.2 = ($$2 a + 9$$) $$-7$$

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$11$$ 11.1 = ($$a + 3$$) $$1$$
$$11$$ 11.2 = ($$a - 3$$) $$1$$
$$169$$ 169.1 = ($$13$$) $$-1$$