# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 16641 Level $$\left(129\right)$$ Label 2.0.7.1-16641.2-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$\ge2$$, even

# Learn more about

## Base field: $$\Q(\sqrt{-7})$$

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

## Form

 Weight 2 Level 16641.2 = $$\left(129\right)$$ Label 2.0.7.1-16641.2-a Dimension: 1 CM: no Base change: yes 6321.2.a.e , 129.2.a.a Newspace: 2.0.7.1-16641.2 (dimension 7) Sign of functional equation: +1 Analytic rank: $$\ge2$$, even

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$0$$
$$2$$ 2.2 = ($$-a + 1$$) $$0$$
$$7$$ 7.1 = ($$-2 a + 1$$) $$-2$$
$$9$$ 9.1 = ($$3$$) $$1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$-5$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-5$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$-1$$
$$23$$ 23.2 = ($$2 a + 3$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$0$$
$$29$$ 29.2 = ($$4 a - 3$$) $$0$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$8$$
$$37$$ 37.2 = ($$4 a + 1$$) $$8$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-1$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-1$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$3$$
$$53$$ 53.2 = ($$4 a - 7$$) $$3$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-15$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-15$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-14$$
$$71$$ 71.2 = ($$2 a + 7$$) $$-14$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-16$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-16$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$0$$
$$107$$ 107.2 = ($$2 a + 9$$) $$0$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$9$$ 9.1 = ($$3$$) $$-1$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$1$$
$$43$$ 43.2 = ($$2 a + 5$$) $$1$$