# Properties

 Base field $$\Q(\sqrt{-11})$$ Weight 2 Level norm 12544 Level $$\left(112\right)$$ Label 2.0.11.1-12544.1-l Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Related objects

## Base field: $$\Q(\sqrt{-11})$$

Generator $$a$$, with minimal polynomial $$x^2 - x + 3$$; class number $$1$$.

## Form

 Weight 2 Level 12544.1 = $$\left(112\right)$$ Label 2.0.11.1-12544.1-l Dimension: 1 CM: no Base change: yes , 112.2.a.c Newspace: 2.0.11.1-12544.1 (dimension 37) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 12

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a$$) $$2$$
$$3$$ 3.2 = ($$a - 1$$) $$2$$
$$4$$ 4.1 = ($$2$$) $$0$$
$$5$$ 5.1 = ($$-a - 1$$) $$0$$
$$5$$ 5.2 = ($$a - 2$$) $$0$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$0$$
$$23$$ 23.1 = ($$a + 4$$) $$0$$
$$23$$ 23.2 = ($$a - 5$$) $$0$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$4$$
$$31$$ 31.2 = ($$3 a + 1$$) $$4$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$2$$
$$37$$ 37.2 = ($$3 a - 5$$) $$2$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$12$$
$$47$$ 47.2 = ($$2 a + 5$$) $$12$$
$$49$$ 49.1 = ($$7$$) $$1$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$6$$
$$53$$ 53.2 = ($$4 a + 1$$) $$6$$
$$59$$ 59.1 = ($$a + 7$$) $$6$$
$$59$$ 59.2 = ($$a - 8$$) $$6$$
$$67$$ 67.1 = ($$-3 a - 5$$) $$4$$
$$67$$ 67.2 = ($$3 a - 8$$) $$4$$
$$71$$ 71.1 = ($$-5 a + 1$$) $$0$$
$$71$$ 71.2 = ($$5 a - 4$$) $$0$$
$$89$$ 89.1 = ($$5 a + 2$$) $$-6$$
$$89$$ 89.2 = ($$5 a - 7$$) $$-6$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$1$$
$$49$$ 49.1 = ($$7$$) $$-1$$