# Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 363 Level $$\left(-22 a + 11\right)$$ Label 2.0.3.1-363.1-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Related objects

## Base field: $$\Q(\sqrt{-3})$$

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

## Form

 Weight 2 Level 363.1 = $$\left(-22 a + 11\right)$$ Label 2.0.3.1-363.1-a Dimension: 1 CM: no Base change: yes 33.2.a.a , 99.2.a.b Newspace: 2.0.3.1-363.1 (dimension 1) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 2

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$-1$$
$$4$$ 4.1 = ($$2$$) $$-3$$
$$7$$ 7.1 = ($$-3 a + 1$$) $$4$$
$$7$$ 7.2 = ($$3 a - 2$$) $$4$$
$$13$$ 13.1 = ($$-4 a + 1$$) $$-2$$
$$13$$ 13.2 = ($$4 a - 3$$) $$-2$$
$$19$$ 19.1 = ($$-5 a + 3$$) $$0$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$0$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$31$$ 31.1 = ($$-6 a + 1$$) $$-8$$
$$31$$ 31.2 = ($$6 a - 5$$) $$-8$$
$$37$$ 37.1 = ($$-7 a + 4$$) $$6$$
$$37$$ 37.2 = ($$-7 a + 3$$) $$6$$
$$43$$ 43.1 = ($$-7 a + 1$$) $$0$$
$$43$$ 43.2 = ($$7 a - 6$$) $$0$$
$$61$$ 61.1 = ($$-9 a + 5$$) $$6$$
$$61$$ 61.2 = ($$-9 a + 4$$) $$6$$
$$67$$ 67.1 = ($$9 a - 7$$) $$-4$$
$$67$$ 67.2 = ($$9 a - 2$$) $$-4$$
$$73$$ 73.1 = ($$-9 a + 1$$) $$-14$$
$$73$$ 73.2 = ($$9 a - 8$$) $$-14$$
$$79$$ 79.1 = ($$10 a - 7$$) $$-4$$
$$79$$ 79.2 = ($$10 a - 3$$) $$-4$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$2$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$2$$
$$103$$ 103.1 = ($$11 a - 9$$) $$8$$
$$103$$ 103.2 = ($$11 a - 2$$) $$8$$
$$109$$ 109.1 = ($$12 a - 5$$) $$-2$$
$$109$$ 109.2 = ($$-12 a + 7$$) $$-2$$
$$121$$ 121.1 = ($$11$$) $$1$$
$$127$$ 127.1 = ($$-13 a + 7$$) $$-4$$
$$127$$ 127.2 = ($$-13 a + 6$$) $$-4$$
$$139$$ 139.1 = ($$13 a - 10$$) $$-8$$
$$139$$ 139.2 = ($$13 a - 3$$) $$-8$$
$$151$$ 151.1 = ($$-14 a + 5$$) $$20$$
$$151$$ 151.2 = ($$-14 a + 9$$) $$20$$
$$157$$ 157.1 = ($$-13 a + 1$$) $$14$$
$$157$$ 157.2 = ($$13 a - 12$$) $$14$$
$$163$$ 163.1 = ($$-14 a + 3$$) $$4$$
$$163$$ 163.2 = ($$-14 a + 11$$) $$4$$
$$181$$ 181.1 = ($$-15 a + 4$$) $$22$$
$$181$$ 181.2 = ($$-15 a + 11$$) $$22$$
$$193$$ 193.1 = ($$16 a - 7$$) $$-14$$
$$193$$ 193.2 = ($$-16 a + 9$$) $$-14$$
$$199$$ 199.1 = ($$15 a - 13$$) $$0$$
$$199$$ 199.2 = ($$15 a - 2$$) $$0$$
$$211$$ 211.1 = ($$-15 a + 1$$) $$0$$
$$211$$ 211.2 = ($$15 a - 14$$) $$0$$
$$223$$ 223.1 = ($$-17 a + 6$$) $$16$$
$$223$$ 223.2 = ($$-17 a + 11$$) $$16$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$1$$
$$121$$ 121.1 = ($$11$$) $$-1$$