# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 34596 Level $$\left(186\right)$$ Label 2.0.7.1-34596.2-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 34596.2 = $$\left(186\right)$$ Label 2.0.7.1-34596.2-e Dimension: 1 CM: no Base change: yes 186.2.a.c , 9114.2.a.t Newspace: 2.0.7.1-34596.2 (dimension 7) 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 = ($$3$$) $$1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$-3$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-3$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$4$$
$$23$$ 23.2 = ($$2 a + 3$$) $$4$$
$$25$$ 25.1 = ($$5$$) $$-9$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$0$$
$$29$$ 29.2 = ($$4 a - 3$$) $$0$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$-2$$
$$37$$ 37.2 = ($$4 a + 1$$) $$-2$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-6$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-6$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$14$$
$$53$$ 53.2 = ($$4 a - 7$$) $$14$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-7$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-7$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-3$$
$$71$$ 71.2 = ($$2 a + 7$$) $$-3$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$15$$
$$79$$ 79.2 = ($$6 a + 1$$) $$15$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$-12$$
$$107$$ 107.2 = ($$2 a + 9$$) $$-12$$
$$109$$ 109.1 = ($$-4 a - 7$$) $$10$$
$$109$$ 109.2 = ($$4 a - 11$$) $$10$$
$$113$$ 113.1 = ($$-8 a + 3$$) $$14$$
$$113$$ 113.2 = ($$-8 a + 5$$) $$14$$
$$127$$ 127.1 = ($$-6 a - 5$$) $$-12$$
$$127$$ 127.2 = ($$6 a - 11$$) $$-12$$
$$137$$ 137.1 = ($$-8 a + 9$$) $$-2$$
$$137$$ 137.2 = ($$8 a + 1$$) $$-2$$
$$149$$ 149.1 = ($$-4 a + 13$$) $$5$$
$$149$$ 149.2 = ($$4 a + 9$$) $$5$$
$$151$$ 151.1 = ($$-2 a + 13$$) $$-3$$
$$151$$ 151.2 = ($$2 a + 11$$) $$-3$$
$$163$$ 163.1 = ($$-6 a + 13$$) $$-21$$
$$163$$ 163.2 = ($$6 a + 7$$) $$-21$$
$$169$$ 169.1 = ($$13$$) $$-25$$
$$179$$ 179.1 = ($$10 a - 7$$) $$-5$$
$$179$$ 179.2 = ($$10 a - 3$$) $$-5$$
$$191$$ 191.1 = ($$-10 a + 1$$) $$-8$$
$$191$$ 191.2 = ($$10 a - 9$$) $$-8$$
$$193$$ 193.1 = ($$-8 a - 5$$) $$-21$$
$$193$$ 193.2 = ($$-8 a + 13$$) $$-21$$
$$197$$ 197.1 = ($$-4 a - 11$$) $$-22$$
$$197$$ 197.2 = ($$4 a - 15$$) $$-22$$
$$211$$ 211.1 = ($$-10 a + 11$$) $$-8$$
$$211$$ 211.2 = ($$10 a + 1$$) $$-8$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$2$$ 2.2 = ($$-a + 1$$) $$-1$$
$$9$$ 9.1 = ($$3$$) $$-1$$
$$961$$ 961.1 = ($$31$$) $$-1$$