# Properties

 Base field $$\Q(\sqrt{-1})$$ Weight 2 Level norm 22050 Level $$\left(105 i + 105\right)$$ Label 2.0.4.1-22050.2-d Dimension 1 CM no Base-change yes Sign +1 Analytic rank $$0$$

# Related objects

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

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

## Form

 Weight 2 Level 22050.2 = $$\left(105 i + 105\right)$$ Label 2.0.4.1-22050.2-d Dimension: 1 CM: no Base change: yes 210.2.a.e , 1680.2.a.j Newspace: 2.0.4.1-22050.2 (dimension 5) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 8

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$1$$
$$5$$ 5.1 = ($$-i - 2$$) $$1$$
$$5$$ 5.2 = ($$2 i + 1$$) $$1$$
$$9$$ 9.1 = ($$3$$) $$1$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$-2$$
$$13$$ 13.2 = ($$2 i + 3$$) $$-2$$
$$17$$ 17.1 = ($$i + 4$$) $$2$$
$$17$$ 17.2 = ($$i - 4$$) $$2$$
$$29$$ 29.1 = ($$-2 i + 5$$) $$-2$$
$$29$$ 29.2 = ($$2 i + 5$$) $$-2$$
$$37$$ 37.1 = ($$i + 6$$) $$6$$
$$37$$ 37.2 = ($$i - 6$$) $$6$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$-6$$
$$41$$ 41.2 = ($$4 i + 5$$) $$-6$$
$$49$$ 49.1 = ($$7$$) $$1$$
$$53$$ 53.1 = ($$-2 i + 7$$) $$-10$$
$$53$$ 53.2 = ($$2 i + 7$$) $$-10$$
$$61$$ 61.1 = ($$-6 i - 5$$) $$14$$
$$61$$ 61.2 = ($$5 i + 6$$) $$14$$
$$73$$ 73.1 = ($$-3 i - 8$$) $$10$$
$$73$$ 73.2 = ($$3 i - 8$$) $$10$$
$$89$$ 89.1 = ($$-5 i + 8$$) $$10$$
$$89$$ 89.2 = ($$-8 i + 5$$) $$10$$
$$97$$ 97.1 = ($$-4 i + 9$$) $$2$$
$$97$$ 97.2 = ($$4 i + 9$$) $$2$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$-1$$
$$9$$ 9.1 = ($$3$$) $$-1$$
$$5$$ 5.1 = ($$-i - 2$$) $$-1$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-1$$
$$49$$ 49.1 = ($$7$$) $$-1$$