Properties

 Label 2.0.8.1-5625.2-b Base field $$\Q(\sqrt{-2})$$ Weight $2$ Level norm $5625$ Level $$\left(75\right)$$ Dimension $1$ CM no Base change yes Sign $-1$ Analytic rank odd

Related objects

Base field: $$\Q(\sqrt{-2})$$

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

Form

 Weight: 2 Level: 5625.2 = $$\left(75\right)$$ Level norm: 5625 Dimension: 1 CM: no Base change: yes 75.2.a.b , 4800.2.a.bz Newspace: 2.0.8.1-5625.2 (dimension 3) Sign of functional equation: $-1$ Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a - 1$$) $$-1$$
$$3$$ 3.2 = ($$a - 1$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$1$$

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$2$$ 2.1 = ($$a$$) $$1$$
$$11$$ 11.1 = ($$a + 3$$) $$-4$$
$$11$$ 11.2 = ($$a - 3$$) $$-4$$
$$17$$ 17.1 = ($$-2 a + 3$$) $$-2$$
$$17$$ 17.2 = ($$2 a + 3$$) $$-2$$
$$19$$ 19.1 = ($$-3 a + 1$$) $$4$$
$$19$$ 19.2 = ($$3 a + 1$$) $$4$$
$$41$$ 41.1 = ($$-4 a - 3$$) $$10$$
$$41$$ 41.2 = ($$4 a - 3$$) $$10$$
$$43$$ 43.1 = ($$-3 a - 5$$) $$-4$$
$$43$$ 43.2 = ($$3 a - 5$$) $$-4$$
$$49$$ 49.1 = ($$7$$) $$-14$$
$$59$$ 59.1 = ($$-5 a + 3$$) $$-4$$
$$59$$ 59.2 = ($$-5 a - 3$$) $$-4$$
$$67$$ 67.1 = ($$-3 a + 7$$) $$-12$$
$$67$$ 67.2 = ($$3 a + 7$$) $$-12$$
$$73$$ 73.1 = ($$-6 a + 1$$) $$-10$$
$$73$$ 73.2 = ($$6 a + 1$$) $$-10$$
$$83$$ 83.1 = ($$a + 9$$) $$-12$$
$$83$$ 83.2 = ($$a - 9$$) $$-12$$
 Display number of eigenvalues