Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 14700 Level $$\left(-140 a + 70\right)$$ Label 2.0.3.1-14700.2-h 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 14700.2 = $$\left(-140 a + 70\right)$$ Label 2.0.3.1-14700.2-h Dimension: 1 CM: no Base change: yes 630.2.a.f , 210.2.a.d Newspace: 2.0.3.1-14700.2 (dimension 9) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 16

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-2 a + 1$$) $$1$$
$$4$$ 4.1 = ($$2$$) $$1$$
$$7$$ 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 = ($$-5 a + 3$$) $$-4$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$1$$
$$31$$ 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 = ($$-7 a + 1$$) $$8$$
$$43$$ 43.2 = ($$7 a - 6$$) $$8$$
$$61$$ 61.1 = ($$-9 a + 5$$) $$2$$
$$61$$ 61.2 = ($$-9 a + 4$$) $$2$$
$$67$$ 67.1 = ($$9 a - 7$$) $$8$$
$$67$$ 67.2 = ($$9 a - 2$$) $$8$$
$$73$$ 73.1 = ($$-9 a + 1$$) $$14$$
$$73$$ 73.2 = ($$9 a - 8$$) $$14$$
$$79$$ 79.1 = ($$10 a - 7$$) $$-16$$
$$79$$ 79.2 = ($$10 a - 3$$) $$-16$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$14$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$14$$

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$
$$3$$ 3.1 = ($$-2 a + 1$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-1$$
$$7$$ 7.1 = ($$-3 a + 1$$) $$-1$$
$$7$$ 7.2 = ($$3 a - 2$$) $$-1$$