# Properties

 Label 2.0.7.1-16384.8-m Base field $$\Q(\sqrt{-7})$$ Weight $2$ Level norm $16384$ Level $$\left(128\right)$$ Dimension $1$ CM no Base change yes Sign $-1$ Analytic rank odd

# Related objects

## Base field: $$\Q(\sqrt{-7})$$

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

## Form

 Weight: 2 Level: 16384.8 = $$\left(128\right)$$ Level norm: 16384 Dimension: 1 CM: no Base change: yes 128.2.a.c , 6272.2.a.b Newspace: 2.0.7.1-16384.8 (dimension 32) Sign of functional equation: $-1$ Analytic rank: odd

## Atkin-Lehner eigenvalues

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

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$7$$ 7.1 = $$\left(-2 a + 1\right)$$ $$4$$
$$9$$ 9.1 = $$\left(3\right)$$ $$-2$$
$$11$$ 11.1 = $$\left(-2 a + 3\right)$$ $$-2$$
$$11$$ 11.2 = $$\left(2 a + 1\right)$$ $$-2$$
$$23$$ 23.1 = $$\left(-2 a + 5\right)$$ $$-4$$
$$23$$ 23.2 = $$\left(2 a + 3\right)$$ $$-4$$
$$25$$ 25.1 = $$\left(5\right)$$ $$-6$$
$$29$$ 29.1 = $$\left(-4 a + 1\right)$$ $$6$$
$$29$$ 29.2 = $$\left(4 a - 3\right)$$ $$6$$
$$37$$ 37.1 = $$\left(-4 a + 5\right)$$ $$-10$$
$$37$$ 37.2 = $$\left(4 a + 1\right)$$ $$-10$$
$$43$$ 43.1 = $$\left(-2 a + 7\right)$$ $$6$$
$$43$$ 43.2 = $$\left(2 a + 5\right)$$ $$6$$
$$53$$ 53.1 = $$\left(-4 a - 3\right)$$ $$6$$
$$53$$ 53.2 = $$\left(4 a - 7\right)$$ $$6$$
$$67$$ 67.1 = $$\left(-6 a + 1\right)$$ $$10$$
$$67$$ 67.2 = $$\left(6 a - 5\right)$$ $$10$$
$$71$$ 71.1 = $$\left(-2 a + 9\right)$$ $$-12$$
$$71$$ 71.2 = $$\left(2 a + 7\right)$$ $$-12$$
$$79$$ 79.1 = $$\left(-6 a + 7\right)$$ $$8$$
 Display number of eigenvalues