# Properties

 Label 2.0.3.1-114244.3-f Base field $$\Q(\sqrt{-3})$$ Weight $2$ Level norm $114244$ Level $$\left(338\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$\ge2$$, even

# Related objects

## Base field: $$\Q(\sqrt{-3})$$

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

## Form

 Weight: 2 Level: 114244.3 = $$\left(338\right)$$ Level norm: 114244 Dimension: 1 CM: no Base change: yes 338.2.a.c , 3042.2.a.k Newspace: 2.0.3.1-114244.3 (dimension 30) Sign of functional equation: $+1$ Analytic rank: $$\ge2$$, even

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = $$\left(2\right)$$ $$-1$$
$$13$$ 13.1 = $$\left(a + 3\right)$$ $$1$$
$$13$$ 13.2 = $$\left(a - 4\right)$$ $$1$$

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$3$$ 3.1 = $$\left(a + 1\right)$$ $$0$$
$$7$$ 7.1 = $$\left(-a - 2\right)$$ $$-4$$
$$7$$ 7.2 = $$\left(a - 3\right)$$ $$-4$$
$$19$$ 19.1 = $$\left(-2 a + 5\right)$$ $$0$$
$$19$$ 19.2 = $$\left(2 a + 3\right)$$ $$0$$
$$25$$ 25.1 = $$\left(5\right)$$ $$-9$$
$$31$$ 31.1 = $$\left(a + 5\right)$$ $$-4$$
$$31$$ 31.2 = $$\left(a - 6\right)$$ $$-4$$
$$37$$ 37.1 = $$\left(-3 a + 7\right)$$ $$-3$$
$$37$$ 37.2 = $$\left(3 a + 4\right)$$ $$-3$$
$$43$$ 43.1 = $$\left(a + 6\right)$$ $$-8$$
$$43$$ 43.2 = $$\left(a - 7\right)$$ $$-8$$
$$61$$ 61.1 = $$\left(-4 a + 9\right)$$ $$7$$
$$61$$ 61.2 = $$\left(4 a + 5\right)$$ $$7$$
$$67$$ 67.1 = $$\left(-2 a + 9\right)$$ $$-4$$
$$67$$ 67.2 = $$\left(2 a + 7\right)$$ $$-4$$
$$73$$ 73.1 = $$\left(a + 8\right)$$ $$-11$$
$$73$$ 73.2 = $$\left(a - 9\right)$$ $$-11$$
$$79$$ 79.1 = $$\left(-3 a + 10\right)$$ $$-4$$
$$79$$ 79.2 = $$\left(3 a + 7\right)$$ $$-4$$
 Display number of eigenvalues