# Properties

 Label 2.0.4.1-1025.2-a2 Base field $$\Q(\sqrt{-1})$$ Weight $2$ Level norm $1025$ Level $$\left(i + 32\right)$$ Dimension $2$ CM not determined Base change no Sign not determined Analytic rank not determined

# Related objects

## Base field: $$\Q(\sqrt{-1})$$

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

## Form

 Weight: 2 Level: 1025.2 = $$\left(i + 32\right)$$ Level norm: 1025 Dimension: 2 CM: not determined Base change: no Newspace: 2.0.4.1-1025.2 (dimension 2) Sign of functional equation: not determined Analytic rank: not determined L-ratio: not determined

Not known

## Hecke eigenvalues

The Hecke eigenfield is $$\Q(z)$$ where $z$ is a root of the defining polynomial: $$x^{2} - 5$$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 15 eigenvalues, all of which are displayed 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 = ($$i + 1$$) $$\frac{1}{2} z + \frac{1}{2}$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-z + 1$$
$$9$$ 9.1 = ($$3$$) $$0$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$z - 1$$
$$13$$ 13.2 = ($$2 i + 3$$) $$-2 z - 1$$
$$17$$ 17.1 = ($$i + 4$$) $$z + 3$$
$$17$$ 17.2 = ($$i - 4$$) $$-2 z + 3$$
$$29$$ 29.1 = ($$-2 i + 5$$) $$2 z$$
$$29$$ 29.2 = ($$2 i + 5$$) $$-2 z + 5$$
$$37$$ 37.1 = ($$i + 6$$) $$3 z + 3$$
$$37$$ 37.2 = ($$i - 6$$) $$-2$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$-3$$
$$49$$ 49.1 = ($$7$$) $$-3 z - 5$$
 Display number of eigenvalues