# Properties

 Label 2.0.4.1-82369.1-b Base field $$\Q(\sqrt{-1})$$ Weight $2$ Level norm $82369$ Level $$\left(63 i + 280\right)$$ Dimension $1$ CM no Base change no Sign $-1$ Analytic rank odd

# Related objects

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

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

## Form

 Weight: 2 Level: 82369.1 = $$\left(63 i + 280\right)$$ Level norm: 82369 Dimension: 1 CM: no Base change: no Newspace: 2.0.4.1-82369.1 (dimension 3) Sign of functional equation: $-1$ Analytic rank: odd

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$49$$ 49.1 = ($$7$$) $$1$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$1$$

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$2$$ 2.1 = ($$i + 1$$) $$1$$
$$5$$ 5.1 = ($$-i - 2$$) $$-1$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-3$$
$$9$$ 9.1 = ($$3$$) $$3$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$-1$$
$$13$$ 13.2 = ($$2 i + 3$$) $$-1$$
$$17$$ 17.1 = ($$i + 4$$) $$0$$
$$17$$ 17.2 = ($$i - 4$$) $$4$$
$$29$$ 29.1 = ($$-2 i + 5$$) $$6$$
$$29$$ 29.2 = ($$2 i + 5$$) $$-8$$
$$37$$ 37.1 = ($$i + 6$$) $$2$$
$$37$$ 37.2 = ($$i - 6$$) $$2$$
$$41$$ 41.2 = ($$4 i + 5$$) $$-12$$
$$53$$ 53.1 = ($$-2 i + 7$$) $$4$$
$$53$$ 53.2 = ($$2 i + 7$$) $$6$$
$$61$$ 61.1 = ($$-6 i - 5$$) $$7$$
$$61$$ 61.2 = ($$5 i + 6$$) $$-3$$
$$73$$ 73.1 = ($$-3 i - 8$$) $$-4$$
$$73$$ 73.2 = ($$3 i - 8$$) $$-6$$
$$89$$ 89.1 = ($$-5 i + 8$$) $$8$$
 Display number of eigenvalues