# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 1089 Level $$\left(33\right)$$ Label 2.0.7.1-1089.2-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Related objects

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

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

## Form

 Weight 2 Level 1089.2 = $$\left(33\right)$$ Label 2.0.7.1-1089.2-a Dimension: 1 CM: no Base change: yes 33.2.a.a , 1617.2.a.j Newspace: 2.0.7.1-1089.2 (dimension 3) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 3

## 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 = ($$-2 a + 1$$) $$4$$
$$9$$ 9.1 = ($$3$$) $$1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$1$$
$$11$$ 11.2 = ($$2 a + 1$$) $$1$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$8$$
$$23$$ 23.2 = ($$2 a + 3$$) $$8$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$-6$$
$$29$$ 29.2 = ($$4 a - 3$$) $$-6$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$6$$
$$37$$ 37.2 = ($$4 a + 1$$) $$6$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$0$$
$$43$$ 43.2 = ($$2 a + 5$$) $$0$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$6$$
$$53$$ 53.2 = ($$4 a - 7$$) $$6$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-4$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-4$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$0$$
$$71$$ 71.2 = ($$2 a + 7$$) $$0$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-4$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-4$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$-12$$
$$107$$ 107.2 = ($$2 a + 9$$) $$-12$$
$$109$$ 109.1 = ($$-4 a - 7$$) $$-2$$
$$109$$ 109.2 = ($$4 a - 11$$) $$-2$$
$$113$$ 113.1 = ($$-8 a + 3$$) $$-6$$
$$113$$ 113.2 = ($$-8 a + 5$$) $$-6$$
$$127$$ 127.1 = ($$-6 a - 5$$) $$-4$$
$$127$$ 127.2 = ($$6 a - 11$$) $$-4$$
$$137$$ 137.1 = ($$-8 a + 9$$) $$2$$
$$137$$ 137.2 = ($$8 a + 1$$) $$2$$
$$149$$ 149.1 = ($$-4 a + 13$$) $$-22$$
$$149$$ 149.2 = ($$4 a + 9$$) $$-22$$
$$151$$ 151.1 = ($$-2 a + 13$$) $$20$$
$$151$$ 151.2 = ($$2 a + 11$$) $$20$$
$$163$$ 163.1 = ($$-6 a + 13$$) $$4$$
$$163$$ 163.2 = ($$6 a + 7$$) $$4$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$10 a - 7$$) $$12$$
$$179$$ 179.2 = ($$10 a - 3$$) $$12$$
$$191$$ 191.1 = ($$-10 a + 1$$) $$8$$
$$191$$ 191.2 = ($$10 a - 9$$) $$8$$
$$193$$ 193.1 = ($$-8 a - 5$$) $$-14$$
$$193$$ 193.2 = ($$-8 a + 13$$) $$-14$$
$$197$$ 197.1 = ($$-4 a - 11$$) $$-14$$
$$197$$ 197.2 = ($$4 a - 15$$) $$-14$$
$$211$$ 211.1 = ($$-10 a + 11$$) $$0$$
$$211$$ 211.2 = ($$10 a + 1$$) $$0$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$9$$ 9.1 = ($$3$$) $$-1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$-1$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-1$$