# Properties

 Label 2.0.4.1-57122.3-a Base field $$\Q(\sqrt{-1})$$ Weight $2$ Level norm $57122$ Level $$\left(169 i + 169\right)$$ Dimension $1$ CM no Base change yes 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: 57122.3 = $$\left(169 i + 169\right)$$ Level norm: 57122 Dimension: 1 CM: no Base change: yes 338.2.a.c , 2704.2.a.i Newspace: 2.0.4.1-57122.3 (dimension 26) Sign of functional equation: $-1$ Analytic rank: odd

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = $$\left(i + 1\right)$$ $$1$$
$$13$$ 13.1 = $$\left(-3 i - 2\right)$$ $$1$$
$$13$$ 13.2 = $$\left(2 i + 3\right)$$ $$1$$

## 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 = $$\left(-i - 2\right)$$ $$1$$
$$5$$ 5.2 = $$\left(2 i + 1\right)$$ $$1$$
$$9$$ 9.1 = $$\left(3\right)$$ $$-6$$
$$17$$ 17.1 = $$\left(i + 4\right)$$ $$3$$
$$17$$ 17.2 = $$\left(i - 4\right)$$ $$3$$
$$29$$ 29.1 = $$\left(-2 i + 5\right)$$ $$-1$$
$$29$$ 29.2 = $$\left(2 i + 5\right)$$ $$-1$$
$$37$$ 37.1 = $$\left(i + 6\right)$$ $$-3$$
$$37$$ 37.2 = $$\left(i - 6\right)$$ $$-3$$
$$41$$ 41.1 = $$\left(-5 i - 4\right)$$ $$9$$
$$41$$ 41.2 = $$\left(4 i + 5\right)$$ $$9$$
$$49$$ 49.1 = $$\left(7\right)$$ $$2$$
$$53$$ 53.1 = $$\left(-2 i + 7\right)$$ $$-9$$
$$53$$ 53.2 = $$\left(2 i + 7\right)$$ $$-9$$
$$61$$ 61.1 = $$\left(-6 i - 5\right)$$ $$7$$
$$61$$ 61.2 = $$\left(5 i + 6\right)$$ $$7$$
$$73$$ 73.1 = $$\left(-3 i - 8\right)$$ $$-11$$
$$73$$ 73.2 = $$\left(3 i - 8\right)$$ $$-11$$
$$89$$ 89.1 = $$\left(-5 i + 8\right)$$ $$6$$
$$89$$ 89.2 = $$\left(-8 i + 5\right)$$ $$6$$
 Display number of eigenvalues