# Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 3072 Level $$\left(-64 a + 32\right)$$ Label 2.0.3.1-3072.1-d Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Related objects

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

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

## Form

 Weight 2 Level 3072.1 = $$\left(-64 a + 32\right)$$ Label 2.0.3.1-3072.1-d Dimension: 1 CM: no Base change: yes 96.2.a.b , 288.2.a.b Newspace: 2.0.3.1-3072.1 (dimension 6) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$1$$
$$4$$ 4.1 = ($$2$$) $$0$$
$$7$$ 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 = ($$-5 a + 3$$) $$-4$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$31$$ 31.1 = ($$-6 a + 1$$) $$4$$
$$31$$ 31.2 = ($$6 a - 5$$) $$4$$
$$37$$ 37.1 = ($$-7 a + 4$$) $$-2$$
$$37$$ 37.2 = ($$-7 a + 3$$) $$-2$$
$$43$$ 43.1 = ($$-7 a + 1$$) $$4$$
$$43$$ 43.2 = ($$7 a - 6$$) $$4$$
$$61$$ 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 = ($$-9 a + 1$$) $$-6$$
$$73$$ 73.2 = ($$9 a - 8$$) $$-6$$
$$79$$ 79.1 = ($$10 a - 7$$) $$4$$
$$79$$ 79.2 = ($$10 a - 3$$) $$4$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$-14$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$-14$$
$$103$$ 103.1 = ($$11 a - 9$$) $$-12$$
$$103$$ 103.2 = ($$11 a - 2$$) $$-12$$
$$109$$ 109.1 = ($$12 a - 5$$) $$14$$
$$109$$ 109.2 = ($$-12 a + 7$$) $$14$$
$$121$$ 121.1 = ($$11$$) $$-6$$
$$127$$ 127.1 = ($$-13 a + 7$$) $$-20$$
$$127$$ 127.2 = ($$-13 a + 6$$) $$-20$$
$$139$$ 139.1 = ($$13 a - 10$$) $$-20$$
$$139$$ 139.2 = ($$13 a - 3$$) $$-20$$
$$151$$ 151.1 = ($$-14 a + 5$$) $$12$$
$$151$$ 151.2 = ($$-14 a + 9$$) $$12$$
$$157$$ 157.1 = ($$-13 a + 1$$) $$-10$$
$$157$$ 157.2 = ($$13 a - 12$$) $$-10$$
$$163$$ 163.1 = ($$-14 a + 3$$) $$-4$$
$$163$$ 163.2 = ($$-14 a + 11$$) $$-4$$
$$181$$ 181.1 = ($$-15 a + 4$$) $$-10$$
$$181$$ 181.2 = ($$-15 a + 11$$) $$-10$$
$$193$$ 193.1 = ($$16 a - 7$$) $$18$$
$$193$$ 193.2 = ($$-16 a + 9$$) $$18$$
$$199$$ 199.1 = ($$15 a - 13$$) $$4$$
$$199$$ 199.2 = ($$15 a - 2$$) $$4$$
$$211$$ 211.1 = ($$-15 a + 1$$) $$20$$
$$211$$ 211.2 = ($$15 a - 14$$) $$20$$
$$223$$ 223.1 = ($$-17 a + 6$$) $$-4$$
$$223$$ 223.2 = ($$-17 a + 11$$) $$-4$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$
$$3$$ 3.1 = ($$-2 a + 1$$) $$-1$$