# Properties

 Base field $$\Q(\sqrt{-3})$$ Weight 2 Level norm 10092 Level $$\left(-116 a + 58\right)$$ Label 2.0.3.1-10092.1-d Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Learn more about

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

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

## Form

 Weight 2 Level 10092.1 = $$\left(-116 a + 58\right)$$ Label 2.0.3.1-10092.1-d Dimension: 1 CM: no Base change: yes 174.2.a.e , 522.2.a.d Newspace: 2.0.3.1-10092.1 (dimension 7) 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 = ($$-4 a + 1$$) $$0$$
$$13$$ 13.2 = ($$4 a - 3$$) $$0$$
$$19$$ 19.1 = ($$-5 a + 3$$) $$-1$$
$$19$$ 19.2 = ($$-5 a + 2$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$-9$$
$$31$$ 31.1 = ($$-6 a + 1$$) $$4$$
$$31$$ 31.2 = ($$6 a - 5$$) $$4$$
$$37$$ 37.1 = ($$-7 a + 4$$) $$3$$
$$37$$ 37.2 = ($$-7 a + 3$$) $$3$$
$$43$$ 43.1 = ($$-7 a + 1$$) $$9$$
$$43$$ 43.2 = ($$7 a - 6$$) $$9$$
$$61$$ 61.1 = ($$-9 a + 5$$) $$6$$
$$61$$ 61.2 = ($$-9 a + 4$$) $$6$$
$$67$$ 67.1 = ($$9 a - 7$$) $$12$$
$$67$$ 67.2 = ($$9 a - 2$$) $$12$$
$$73$$ 73.1 = ($$-9 a + 1$$) $$-10$$
$$73$$ 73.2 = ($$9 a - 8$$) $$-10$$
$$79$$ 79.1 = ($$10 a - 7$$) $$10$$
$$79$$ 79.2 = ($$10 a - 3$$) $$10$$
$$97$$ 97.1 = ($$-11 a + 3$$) $$0$$
$$97$$ 97.2 = ($$-11 a + 8$$) $$0$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$
$$3$$ 3.1 = ($$-2 a + 1$$) $$-1$$
$$841$$ 841.1 = ($$29$$) $$-1$$