Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 12675 Level $$\left(-130 a + 65\right)$$ Label 2.0.3.1-12675.2-b 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 12675.2 = $$\left(-130 a + 65\right)$$ Label 2.0.3.1-12675.2-b Dimension: 1 CM: no Base change: yes 195.2.a.a , 585.2.a.g Newspace: 2.0.3.1-12675.2 (dimension 7) 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 = ($$2$$) $$-3$$
$$7$$ 7.1 = ($$-3 a + 1$$) $$0$$
$$7$$ 7.2 = ($$3 a - 2$$) $$0$$
$$13$$ 13.1 = ($$-4 a + 1$$) $$1$$
$$13$$ 13.2 = ($$4 a - 3$$) $$1$$
$$19$$ 19.1 = ($$-5 a + 3$$) $$-4$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$1$$
$$31$$ 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 = ($$-7 a + 1$$) $$-4$$
$$43$$ 43.2 = ($$7 a - 6$$) $$-4$$
$$61$$ 61.1 = ($$-9 a + 5$$) $$-2$$
$$61$$ 61.2 = ($$-9 a + 4$$) $$-2$$
$$67$$ 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 = ($$10 a - 7$$) $$16$$
$$79$$ 79.2 = ($$10 a - 3$$) $$16$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$18$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$18$$

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-1$$
$$13$$ 13.1 = ($$-4 a + 1$$) $$-1$$
$$13$$ 13.2 = ($$4 a - 3$$) $$-1$$