Properties

 Label 2.0.3.1-37632.2-a Base field $$\Q(\sqrt{-3})$$ Weight $2$ Level norm $37632$ Level $$\left(112 a + 112\right)$$ Dimension $1$ CM no Base change yes Sign $-1$ Analytic rank odd

Related objects

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

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

Form

 Weight: 2 Level: 37632.2 = $$\left(112 a + 112\right)$$ Level norm: 37632 Dimension: 1 CM: no Base change: yes 1008.2.a.g , 336.2.a.b Newspace: 2.0.3.1-37632.2 (dimension 18) Sign of functional equation: $-1$ Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = $$\left(a + 1\right)$$ $$1$$
$$4$$ 4.1 = $$\left(2\right)$$ $$1$$
$$7$$ 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$13$$ 13.1 = $$\left(a + 3\right)$$ $$2$$
$$13$$ 13.2 = $$\left(a - 4\right)$$ $$2$$
$$19$$ 19.1 = $$\left(-2 a + 5\right)$$ $$4$$
$$19$$ 19.2 = $$\left(2 a + 3\right)$$ $$4$$
$$25$$ 25.1 = $$\left(5\right)$$ $$-10$$
$$31$$ 31.1 = $$\left(a + 5\right)$$ $$-8$$
$$31$$ 31.2 = $$\left(a - 6\right)$$ $$-8$$
$$37$$ 37.1 = $$\left(-3 a + 7\right)$$ $$2$$
$$37$$ 37.2 = $$\left(3 a + 4\right)$$ $$2$$
$$43$$ 43.1 = $$\left(a + 6\right)$$ $$4$$
$$43$$ 43.2 = $$\left(a - 7\right)$$ $$4$$
$$61$$ 61.1 = $$\left(-4 a + 9\right)$$ $$-10$$
$$61$$ 61.2 = $$\left(4 a + 5\right)$$ $$-10$$
$$67$$ 67.1 = $$\left(-2 a + 9\right)$$ $$-8$$
$$67$$ 67.2 = $$\left(2 a + 7\right)$$ $$-8$$
$$73$$ 73.1 = $$\left(a + 8\right)$$ $$-10$$
$$73$$ 73.2 = $$\left(a - 9\right)$$ $$-10$$
$$79$$ 79.1 = $$\left(-3 a + 10\right)$$ $$4$$
$$79$$ 79.2 = $$\left(3 a + 7\right)$$ $$4$$
$$97$$ 97.1 = $$\left(-3 a - 8\right)$$ $$-10$$
 Display number of eigenvalues