# Properties

 Label 2.0.7.1-36288.4-f Base field $$\Q(\sqrt{-7})$$ Weight $2$ Level norm $36288$ Level $$\left(-144 a + 72\right)$$ Dimension $1$ CM no Base change yes Sign $+1$ Analytic rank $$0$$

# Related objects

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

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

## Form

 Weight: 2 Level: 36288.4 = $$\left(-144 a + 72\right)$$ Level norm: 36288 Dimension: 1 CM: no Base change: yes 3528.2.a.b , 504.2.a.h Newspace: 2.0.7.1-36288.4 (dimension 12) Sign of functional equation: $+1$ Analytic rank: $$0$$ L-ratio: 2

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$2$$ 2.2 = ($$-a + 1$$) $$-1$$
$$9$$ 9.1 = ($$3$$) $$-1$$
$$7$$ 7.1 = ($$-2 a + 1$$) $$1$$

## 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$11$$ 11.1 = ($$-2 a + 3$$) $$0$$
$$11$$ 11.2 = ($$2 a + 1$$) $$0$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$-8$$
$$23$$ 23.2 = ($$2 a + 3$$) $$-8$$
$$25$$ 25.1 = ($$5$$) $$6$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$-2$$
$$29$$ 29.2 = ($$4 a - 3$$) $$-2$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$-6$$
$$37$$ 37.2 = ($$4 a + 1$$) $$-6$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$8$$
$$43$$ 43.2 = ($$2 a + 5$$) $$8$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$10$$
$$53$$ 53.2 = ($$4 a - 7$$) $$10$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$-12$$
$$67$$ 67.2 = ($$6 a - 5$$) $$-12$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$0$$
$$71$$ 71.2 = ($$2 a + 7$$) $$0$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$-8$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-8$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$12$$
 Display number of eigenvalues