# Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 12544 Level $$\left(112\right)$$ Label 2.0.3.1-12544.2-j Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

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

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

## Form

 Weight 2 Level 12544.2 = $$\left(112\right)$$ Label 2.0.3.1-12544.2-j Dimension: 1 CM: no Base change: yes 1008.2.a.d , 112.2.a.b Newspace: 2.0.3.1-12544.2 (dimension 13) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$0$$
$$4$$ 4.1 = ($$2$$) $$0$$
$$7$$ 7.1 = ($$-3 a + 1$$) $$1$$
$$7$$ 7.2 = ($$3 a - 2$$) $$1$$
$$13$$ 13.1 = ($$-4 a + 1$$) $$2$$
$$13$$ 13.2 = ($$4 a - 3$$) $$2$$
$$19$$ 19.1 = ($$-5 a + 3$$) $$-8$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-8$$
$$25$$ 25.1 = ($$5$$) $$-6$$
$$31$$ 31.1 = ($$-6 a + 1$$) $$-8$$
$$31$$ 31.2 = ($$6 a - 5$$) $$-8$$
$$37$$ 37.1 = ($$-7 a + 4$$) $$-2$$
$$37$$ 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 = ($$-9 a + 1$$) $$10$$
$$73$$ 73.2 = ($$9 a - 8$$) $$10$$
$$79$$ 79.1 = ($$10 a - 7$$) $$-16$$
$$79$$ 79.2 = ($$10 a - 3$$) $$-16$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$-6$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$-6$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$1$$
$$7$$ 7.1 = ($$-3 a + 1$$) $$-1$$
$$7$$ 7.2 = ($$3 a - 2$$) $$-1$$