# Properties

 Base field $$\Q(\sqrt{-1})$$ Weight 2 Level norm 377 Level $$\left(16 i - 11\right)$$ Label 2.0.4.1-377.1-a2 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 377.1 = $$\left(16 i - 11\right)$$ Label 2.0.4.1-377.1-a2 Dimension: 2 CM: not determined Base change: no Newspace: 2.0.4.1-377.1 (dimension 3) Sign of functional equation: not determined Analytic rank: not determined L-ratio: not determined

## Hecke eigenvalues

The Hecke eigenfield is $$\Q(z)$$ where $z$ is a root of the defining polynomial: $$x^{2} - 2$$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$-z$$
$$5$$ 5.1 = ($$-i - 2$$) $$2 z$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-1$$
$$9$$ 9.1 = ($$3$$) $$2 z + 2$$
$$13$$ 13.1 = ($$-3 i - 2$$) not known
$$13$$ 13.2 = ($$2 i + 3$$) $$2 z - 1$$
$$17$$ 17.1 = ($$i + 4$$) $$4$$
$$17$$ 17.2 = ($$i - 4$$) $$2 z + 3$$
$$29$$ 29.1 = ($$-2 i + 5$$) not known
$$29$$ 29.2 = ($$2 i + 5$$) $$2 z + 1$$
$$37$$ 37.1 = ($$i + 6$$) $$-2 z - 5$$
$$37$$ 37.2 = ($$i - 6$$) $$-4 z + 5$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$-4 z + 5$$
$$41$$ 41.2 = ($$4 i + 5$$) $$2 z + 1$$
$$49$$ 49.1 = ($$7$$) $$2 z$$

Not known