# Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 16384 Level $$\left(128\right)$$ Label 2.0.3.1-16384.1-a Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$\ge2$$, even

# Related objects

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

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

## Form

 Weight 2 Level 16384.1 = $$\left(128\right)$$ Label 2.0.3.1-16384.1-a Dimension: 1 CM: no Base change: yes 1152.2.a.m , 128.2.a.a Newspace: 2.0.3.1-16384.1 (dimension 16) Sign of functional equation: +1 Analytic rank: $$\ge2$$, even

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$-2$$
$$4$$ 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 = ($$-5 a + 3$$) $$-2$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-2$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$31$$ 31.1 = ($$-6 a + 1$$) $$0$$
$$31$$ 31.2 = ($$6 a - 5$$) $$0$$
$$37$$ 37.1 = ($$-7 a + 4$$) $$-10$$
$$37$$ 37.2 = ($$-7 a + 3$$) $$-10$$
$$43$$ 43.1 = ($$-7 a + 1$$) $$-6$$
$$43$$ 43.2 = ($$7 a - 6$$) $$-6$$
$$61$$ 61.1 = ($$-9 a + 5$$) $$-2$$
$$61$$ 61.2 = ($$-9 a + 4$$) $$-2$$
$$67$$ 67.1 = ($$9 a - 7$$) $$-10$$
$$67$$ 67.2 = ($$9 a - 2$$) $$-10$$
$$73$$ 73.1 = ($$-9 a + 1$$) $$14$$
$$73$$ 73.2 = ($$9 a - 8$$) $$14$$
$$79$$ 79.1 = ($$10 a - 7$$) $$-8$$
$$79$$ 79.2 = ($$10 a - 3$$) $$-8$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$-2$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$-2$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$