# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 26244 Level $$\left(162\right)$$ Label 2.0.7.1-26244.2-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 26244.2 = $$\left(162\right)$$ Label 2.0.7.1-26244.2-b Dimension: 1 CM: no Base change: yes 7938.2.a.i , 162.2.a.b Newspace: 2.0.7.1-26244.2 (dimension 28) 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 = ($$-2 a + 1$$) $$2$$
$$9$$ 9.1 = ($$3$$) $$0$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$3$$
$$11$$ 11.2 = ($$2 a + 1$$) $$3$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$6$$
$$23$$ 23.2 = ($$2 a + 3$$) $$6$$
$$25$$ 25.1 = ($$5$$) $$-10$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$-6$$
$$29$$ 29.2 = ($$4 a - 3$$) $$-6$$
$$37$$ 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 = ($$-4 a - 3$$) $$-12$$
$$53$$ 53.2 = ($$4 a - 7$$) $$-12$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$5$$
$$67$$ 67.2 = ($$6 a - 5$$) $$5$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$12$$
$$71$$ 71.2 = ($$2 a + 7$$) $$12$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-4$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-4$$
$$107$$ 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 = ($$-a + 1$$) $$1$$
$$9$$ 9.1 = ($$3$$) $$1$$