# Properties

 Label 2.0.4.1-58482.1-b Base field $$\Q(\sqrt{-1})$$ Weight $2$ Level norm $58482$ Level $$\left(171 i + 171\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$0$$

# Related objects

## Base field: $$\Q(\sqrt{-1})$$

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

## Form

 Weight: 2 Level: 58482.1 = $$\left(171 i + 171\right)$$ Level norm: 58482 Dimension: 1 CM: no Base change: yes 2736.2.a.d , 342.2.a.b Newspace: 2.0.4.1-58482.1 (dimension 7) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 8

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$1$$
$$9$$ 9.1 = ($$3$$) $$1$$
$$361$$ 361.1 = ($$19$$) $$-1$$

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$5$$ 5.1 = ($$-i - 2$$) $$-2$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-2$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$2$$
$$13$$ 13.2 = ($$2 i + 3$$) $$2$$
$$17$$ 17.1 = ($$i + 4$$) $$6$$
$$17$$ 17.2 = ($$i - 4$$) $$6$$
$$29$$ 29.1 = ($$-2 i + 5$$) $$2$$
$$29$$ 29.2 = ($$2 i + 5$$) $$2$$
$$37$$ 37.1 = ($$i + 6$$) $$10$$
$$37$$ 37.2 = ($$i - 6$$) $$10$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$-10$$
$$41$$ 41.2 = ($$4 i + 5$$) $$-10$$
$$49$$ 49.1 = ($$7$$) $$-14$$
$$53$$ 53.1 = ($$-2 i + 7$$) $$10$$
$$53$$ 53.2 = ($$2 i + 7$$) $$10$$
$$61$$ 61.1 = ($$-6 i - 5$$) $$14$$
$$61$$ 61.2 = ($$5 i + 6$$) $$14$$
$$73$$ 73.1 = ($$-3 i - 8$$) $$-6$$
$$73$$ 73.2 = ($$3 i - 8$$) $$-6$$
$$89$$ 89.1 = ($$-5 i + 8$$) $$6$$
$$89$$ 89.2 = ($$-8 i + 5$$) $$6$$
 Display number of eigenvalues