# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 31684 Level $$\left(178\right)$$ Label 2.0.7.1-31684.2-b Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$\ge2$$, even

# Related objects

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

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

## Form

 Weight 2 Level 31684.2 = $$\left(178\right)$$ Label 2.0.7.1-31684.2-b Dimension: 1 CM: no Base change: yes 178.2.a.b , 8722.2.a.m Newspace: 2.0.7.1-31684.2 (dimension 13) Sign of functional equation: +1 Analytic rank: $$\ge2$$, even

## 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 = ($$3$$) $$-5$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$-6$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-6$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$-3$$
$$23$$ 23.2 = ($$2 a + 3$$) $$-3$$
$$25$$ 25.1 = ($$5$$) $$-1$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$0$$
$$29$$ 29.2 = ($$4 a - 3$$) $$0$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$-10$$
$$37$$ 37.2 = ($$4 a + 1$$) $$-10$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-1$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-1$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$9$$
$$53$$ 53.2 = ($$4 a - 7$$) $$9$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-4$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-4$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-6$$
$$71$$ 71.2 = ($$2 a + 7$$) $$-6$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-10$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-10$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$18$$
$$107$$ 107.2 = ($$2 a + 9$$) $$18$$
$$109$$ 109.1 = ($$-4 a - 7$$) $$-7$$
$$109$$ 109.2 = ($$4 a - 11$$) $$-7$$
$$113$$ 113.1 = ($$-8 a + 3$$) $$-6$$
$$113$$ 113.2 = ($$-8 a + 5$$) $$-6$$
$$127$$ 127.1 = ($$-6 a - 5$$) $$-7$$
$$127$$ 127.2 = ($$6 a - 11$$) $$-7$$
$$137$$ 137.1 = ($$-8 a + 9$$) $$18$$
$$137$$ 137.2 = ($$8 a + 1$$) $$18$$
$$149$$ 149.1 = ($$-4 a + 13$$) $$-12$$
$$149$$ 149.2 = ($$4 a + 9$$) $$-12$$
$$151$$ 151.1 = ($$-2 a + 13$$) $$-16$$
$$151$$ 151.2 = ($$2 a + 11$$) $$-16$$
$$163$$ 163.1 = ($$-6 a + 13$$) $$-1$$
$$163$$ 163.2 = ($$6 a + 7$$) $$-1$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$10 a - 7$$) $$18$$
$$179$$ 179.2 = ($$10 a - 3$$) $$18$$
$$191$$ 191.1 = ($$-10 a + 1$$) $$-3$$
$$191$$ 191.2 = ($$10 a - 9$$) $$-3$$
$$193$$ 193.1 = ($$-8 a - 5$$) $$-22$$
$$193$$ 193.2 = ($$-8 a + 13$$) $$-22$$
$$197$$ 197.1 = ($$-4 a - 11$$) $$0$$
$$197$$ 197.2 = ($$4 a - 15$$) $$0$$
$$211$$ 211.1 = ($$-10 a + 11$$) $$-4$$
$$211$$ 211.2 = ($$10 a + 1$$) $$-4$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$2$$ 2.2 = ($$-a + 1$$) $$-1$$
$$7921$$ 7921.1 = ($$89$$) $$-1$$