Properties

 Label 2.0.3.1-21609.3-d Base field $$\Q(\sqrt{-3})$$ Weight $2$ Level norm $21609$ Level $$\left(147\right)$$ Dimension $1$ CM $-7$ Base change yes Sign $+1$ Analytic rank $$0$$

Related objects

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

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

Form

 Weight: 2 Level: 21609.3 = $$\left(147\right)$$ Level norm: 21609 Dimension: 1 CM: $-7$ Base change: yes, of a form over $$\mathbb{Q}$$ with coefficients in $$\mathbb{Q}(\sqrt{7})$$ Newspace: 2.0.3.1-21609.3 (dimension 8) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 2

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = $$\left(a + 1\right)$$ $$-1$$
$$7$$ 7.1 = $$\left(-a - 2\right)$$ $$-1$$
$$7$$ 7.2 = $$\left(a - 3\right)$$ $$-1$$

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$4$$ 4.1 = $$\left(2\right)$$ $$3$$
$$13$$ 13.1 = $$\left(a + 3\right)$$ $$0$$
$$13$$ 13.2 = $$\left(a - 4\right)$$ $$0$$
$$19$$ 19.1 = $$\left(-2 a + 5\right)$$ $$0$$
$$19$$ 19.2 = $$\left(2 a + 3\right)$$ $$0$$
$$25$$ 25.1 = $$\left(5\right)$$ $$-10$$
$$31$$ 31.1 = $$\left(a + 5\right)$$ $$0$$
$$31$$ 31.2 = $$\left(a - 6\right)$$ $$0$$
$$37$$ 37.1 = $$\left(-3 a + 7\right)$$ $$6$$
$$37$$ 37.2 = $$\left(3 a + 4\right)$$ $$6$$
$$43$$ 43.1 = $$\left(a + 6\right)$$ $$12$$
$$43$$ 43.2 = $$\left(a - 7\right)$$ $$12$$
$$61$$ 61.1 = $$\left(-4 a + 9\right)$$ $$0$$
$$61$$ 61.2 = $$\left(4 a + 5\right)$$ $$0$$
$$67$$ 67.1 = $$\left(-2 a + 9\right)$$ $$4$$
$$67$$ 67.2 = $$\left(2 a + 7\right)$$ $$4$$
$$73$$ 73.1 = $$\left(a + 8\right)$$ $$0$$
$$73$$ 73.2 = $$\left(a - 9\right)$$ $$0$$
$$79$$ 79.1 = $$\left(-3 a + 10\right)$$ $$8$$
$$79$$ 79.2 = $$\left(3 a + 7\right)$$ $$8$$
 Display number of eigenvalues