# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 19044 Level $$\left(138\right)$$ Label 2.0.7.1-19044.5-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$\ge2$$, even

# Related objects

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

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

## Form

 Weight 2 Level 19044.5 = $$\left(138\right)$$ Label 2.0.7.1-19044.5-a Dimension: 1 CM: no Base change: yes 6762.2.a.q , 138.2.a.a Newspace: 2.0.7.1-19044.5 (dimension 13) Sign of functional equation: +1 Analytic rank: $$\ge2$$, even

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$2$$ 2.2 = ($$-a + 1$$) $$-1$$
$$7$$ 7.1 = ($$-2 a + 1$$) $$-2$$
$$9$$ 9.1 = ($$3$$) $$1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$-6$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-6$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$-1$$
$$23$$ 23.2 = ($$2 a + 3$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$6$$
$$29$$ 29.2 = ($$4 a - 3$$) $$6$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$0$$
$$37$$ 37.2 = ($$4 a + 1$$) $$0$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-12$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-12$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$2$$
$$53$$ 53.2 = ($$4 a - 7$$) $$2$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-12$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-12$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$0$$
$$71$$ 71.2 = ($$2 a + 7$$) $$0$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-6$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-6$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$14$$
$$107$$ 107.2 = ($$2 a + 9$$) $$14$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$1$$
$$2$$ 2.2 = ($$-a + 1$$) $$1$$
$$9$$ 9.1 = ($$3$$) $$-1$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$1$$
$$23$$ 23.2 = ($$2 a + 3$$) $$1$$