# Properties

 Label 2.0.15.1-100.2-b Base field $$\Q(\sqrt{-15})$$ Weight $2$ Level norm $100$ Level $$\left(10\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$0$$

# Related objects

## Base field: $$\Q(\sqrt{-15})$$

Generator $$a$$, with minimal polynomial $$x^2 - x + 4$$; class number $$2$$.

## Form

 Weight: 2 Level: 100.2 = $$\left(10\right)$$ Level norm: 100 Dimension: 1 CM: no Base change: yes 50.2.a.b , 450.2.a.g Newspace: 2.0.15.1-100.2 (dimension 2) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 2

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = $$\left(2, a\right)$$ $$-1$$
$$2$$ 2.2 = $$\left(2, a + 1\right)$$ $$-1$$
$$5$$ 5.1 = $$\left(5, a + 2\right)$$ $$1$$

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 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 = $$\left(3, a + 1\right)$$ $$-1$$
$$17$$ 17.1 = $$\left(17, a + 5\right)$$ $$3$$
$$17$$ 17.2 = $$\left(17, a + 11\right)$$ $$3$$
$$19$$ 19.1 = $$\left(-2 a + 3\right)$$ $$5$$
$$19$$ 19.2 = $$\left(2 a + 1\right)$$ $$5$$
$$23$$ 23.1 = $$\left(23, a + 6\right)$$ $$-6$$
$$23$$ 23.2 = $$\left(23, a + 16\right)$$ $$-6$$
$$31$$ 31.1 = $$\left(-2 a + 5\right)$$ $$2$$
$$31$$ 31.2 = $$\left(2 a + 3\right)$$ $$2$$
$$47$$ 47.1 = $$\left(47, a + 9\right)$$ $$-12$$
$$47$$ 47.2 = $$\left(47, a + 37\right)$$ $$-12$$
$$49$$ 49.1 = $$\left(7\right)$$ $$-10$$
$$53$$ 53.1 = $$\left(53, a + 20\right)$$ $$-6$$
$$53$$ 53.2 = $$\left(53, a + 32\right)$$ $$-6$$
$$61$$ 61.1 = $$\left(-4 a + 1\right)$$ $$2$$
$$61$$ 61.2 = $$\left(4 a - 3\right)$$ $$2$$
$$79$$ 79.1 = $$\left(-2 a + 9\right)$$ $$-10$$
$$79$$ 79.2 = $$\left(2 a + 7\right)$$ $$-10$$
$$83$$ 83.1 = $$\left(83, a + 31\right)$$ $$9$$
$$83$$ 83.2 = $$\left(83, a + 51\right)$$ $$9$$
 Display number of eigenvalues