# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 16384 Level $$\left(128\right)$$ Label 2.0.7.1-16384.8-b 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 16384.8 = $$\left(128\right)$$ Label 2.0.7.1-16384.8-b Dimension: 1 CM: no Base change: yes 128.2.a.a , 6272.2.a.h Newspace: 2.0.7.1-16384.8 (dimension 32) Sign of functional equation: -1 Analytic rank: odd

## 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 = ($$-2 a + 1$$) $$-4$$
$$9$$ 9.1 = ($$3$$) $$-2$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$2$$
$$11$$ 11.2 = ($$2 a + 1$$) $$2$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$4$$
$$23$$ 23.2 = ($$2 a + 3$$) $$4$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$6$$
$$29$$ 29.2 = ($$4 a - 3$$) $$6$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$-10$$
$$37$$ 37.2 = ($$4 a + 1$$) $$-10$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-6$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-6$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$6$$
$$53$$ 53.2 = ($$4 a - 7$$) $$6$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-10$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-10$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$12$$
$$71$$ 71.2 = ($$2 a + 7$$) $$12$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-8$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-8$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$2$$
$$107$$ 107.2 = ($$2 a + 9$$) $$2$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$1$$
$$2$$ 2.2 = ($$-a + 1$$) $$1$$