Properties

 Label 2.0.11.1-19404.2-k Base field $$\Q(\sqrt{-11})$$ Weight $2$ Level norm $19404$ Level $$\left(-84 a + 42\right)$$ Dimension $1$ CM no Base change yes Sign $-1$ Analytic rank odd

Related objects

Base field: $$\Q(\sqrt{-11})$$

Generator $$a$$, with minimal polynomial $$x^2 - x + 3$$; class number $$1$$.

Form

 Weight: 2 Level: 19404.2 = $$\left(-84 a + 42\right)$$ Level norm: 19404 Dimension: 1 CM: no Base change: yes 5082.2.a.ba , 462.2.a.d Newspace: 2.0.11.1-19404.2 (dimension 17) Sign of functional equation: $-1$ Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = $$\left(-a\right)$$ $$-1$$
$$3$$ 3.2 = $$\left(a - 1\right)$$ $$-1$$
$$4$$ 4.1 = $$\left(2\right)$$ $$-1$$
$$11$$ 11.1 = $$\left(-2 a + 1\right)$$ $$1$$
$$49$$ 49.1 = $$\left(7\right)$$ $$-1$$

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 = $$\left(-a - 1\right)$$ $$0$$
$$5$$ 5.2 = $$\left(a - 2\right)$$ $$0$$
$$23$$ 23.1 = $$\left(a + 4\right)$$ $$-4$$
$$23$$ 23.2 = $$\left(a - 5\right)$$ $$-4$$
$$31$$ 31.1 = $$\left(-3 a + 4\right)$$ $$-2$$
$$31$$ 31.2 = $$\left(3 a + 1\right)$$ $$-2$$
$$37$$ 37.1 = $$\left(-3 a - 2\right)$$ $$10$$
$$37$$ 37.2 = $$\left(3 a - 5\right)$$ $$10$$
$$47$$ 47.1 = $$\left(-2 a + 7\right)$$ $$-6$$
$$47$$ 47.2 = $$\left(2 a + 5\right)$$ $$-6$$
$$53$$ 53.1 = $$\left(-4 a + 5\right)$$ $$-10$$
$$53$$ 53.2 = $$\left(4 a + 1\right)$$ $$-10$$
$$59$$ 59.1 = $$\left(a + 7\right)$$ $$0$$
$$59$$ 59.2 = $$\left(a - 8\right)$$ $$0$$
$$67$$ 67.1 = $$\left(-3 a - 5\right)$$ $$-4$$
$$67$$ 67.2 = $$\left(3 a - 8\right)$$ $$-4$$
$$71$$ 71.1 = $$\left(-5 a + 1\right)$$ $$16$$
$$71$$ 71.2 = $$\left(5 a - 4\right)$$ $$16$$
$$89$$ 89.1 = $$\left(5 a + 2\right)$$ $$-6$$
$$89$$ 89.2 = $$\left(5 a - 7\right)$$ $$-6$$
 Display number of eigenvalues