# Properties

 Label 2.0.163.1-256.1-a Base field $$\Q(\sqrt{-163})$$ Weight $2$ Level norm $256$ Level $$\left(16\right)$$ Dimension $1$ CM no Base change no Sign $+1$ Analytic rank $$0$$

# Related objects

## Base field: $$\Q(\sqrt{-163})$$

Generator $$a$$, with minimal polynomial $$x^2 - x + 41$$; class number $$1$$.

## Form

 Weight: 2 Level: 256.1 = $$\left(16\right)$$ Level norm: 256 Dimension: 1 CM: no Base change: no, but is a twist of the base change of a form over $$\mathbb{Q}$$ Newspace: 2.0.163.1-256.1 (dimension 78) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 4

## Atkin-Lehner eigenvalues

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

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$9$$ 9.1 = ($$3$$) $$-6$$
$$25$$ 25.1 = ($$5$$) $$1$$
$$41$$ 41.1 = ($$-a$$) $$5$$
$$41$$ 41.2 = ($$a - 1$$) $$5$$
$$43$$ 43.1 = ($$a + 1$$) $$-9$$
$$43$$ 43.2 = ($$a - 2$$) $$9$$
$$47$$ 47.1 = ($$a + 2$$) $$8$$
$$47$$ 47.2 = ($$a - 3$$) $$-8$$
$$49$$ 49.1 = ($$7$$) $$-5$$
$$53$$ 53.1 = ($$a + 3$$) $$4$$
$$53$$ 53.2 = ($$a - 4$$) $$4$$
$$61$$ 61.1 = ($$a + 4$$) $$6$$
$$61$$ 61.2 = ($$a - 5$$) $$6$$
$$71$$ 71.1 = ($$a + 5$$) $$8$$
$$71$$ 71.2 = ($$a - 6$$) $$-8$$
$$83$$ 83.1 = ($$a + 6$$) $$-11$$
$$83$$ 83.2 = ($$a - 7$$) $$11$$
$$97$$ 97.1 = ($$a + 7$$) $$-15$$
$$97$$ 97.2 = ($$a - 8$$) $$-15$$
$$113$$ 113.1 = ($$a + 8$$) $$-2$$
 Display number of eigenvalues