# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 20164 Level $$\left(142\right)$$ Label 2.0.7.1-20164.5-e Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Related objects

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

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

## Form

 Weight 2 Level 20164.5 = $$\left(142\right)$$ Label 2.0.7.1-20164.5-e Dimension: 1 CM: no Base change: yes 142.2.a.e , 6958.2.a.j Newspace: 2.0.7.1-20164.5 (dimension 11) Sign of functional equation: -1 Analytic rank: odd

## 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 = ($$-2 a + 1$$) $$-1$$
$$9$$ 9.1 = ($$3$$) $$-5$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$0$$
$$11$$ 11.2 = ($$2 a + 1$$) $$0$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$3$$
$$23$$ 23.2 = ($$2 a + 3$$) $$3$$
$$25$$ 25.1 = ($$5$$) $$-10$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$0$$
$$29$$ 29.2 = ($$4 a - 3$$) $$0$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$-4$$
$$37$$ 37.2 = ($$4 a + 1$$) $$-4$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-1$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-1$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$6$$
$$53$$ 53.2 = ($$4 a - 7$$) $$6$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$8$$
$$67$$ 67.2 = ($$6 a - 5$$) $$8$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-1$$
$$71$$ 71.2 = ($$2 a + 7$$) $$-1$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$8$$
$$79$$ 79.2 = ($$6 a + 1$$) $$8$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$-3$$
$$107$$ 107.2 = ($$2 a + 9$$) $$-3$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$2$$ 2.2 = ($$-a + 1$$) $$-1$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$1$$
$$71$$ 71.2 = ($$2 a + 7$$) $$1$$