# Properties

 Base field $$\Q(\sqrt{-1})$$ Weight 2 Level norm 13122 Level $$\left(81 i + 81\right)$$ Label 2.0.4.1-13122.1-b Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Related objects

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

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

## Form

 Weight 2 Level 13122.1 = $$\left(81 i + 81\right)$$ Label 2.0.4.1-13122.1-b Dimension: 1 CM: no Base change: yes 1296.2.a.f , 162.2.a.b Newspace: 2.0.4.1-13122.1 (dimension 4) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$-1$$
$$5$$ 5.1 = ($$-i - 2$$) $$0$$
$$5$$ 5.2 = ($$2 i + 1$$) $$0$$
$$9$$ 9.1 = ($$3$$) $$0$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$2$$
$$13$$ 13.2 = ($$2 i + 3$$) $$2$$
$$17$$ 17.1 = ($$i + 4$$) $$3$$
$$17$$ 17.2 = ($$i - 4$$) $$3$$
$$29$$ 29.1 = ($$-2 i + 5$$) $$-6$$
$$29$$ 29.2 = ($$2 i + 5$$) $$-6$$
$$37$$ 37.1 = ($$i + 6$$) $$-4$$
$$37$$ 37.2 = ($$i - 6$$) $$-4$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$-9$$
$$41$$ 41.2 = ($$4 i + 5$$) $$-9$$
$$49$$ 49.1 = ($$7$$) $$-10$$
$$53$$ 53.1 = ($$-2 i + 7$$) $$-12$$
$$53$$ 53.2 = ($$2 i + 7$$) $$-12$$
$$61$$ 61.1 = ($$-6 i - 5$$) $$8$$
$$61$$ 61.2 = ($$5 i + 6$$) $$8$$
$$73$$ 73.1 = ($$-3 i - 8$$) $$11$$
$$73$$ 73.2 = ($$3 i - 8$$) $$11$$
$$89$$ 89.1 = ($$-5 i + 8$$) $$-6$$
$$89$$ 89.2 = ($$-8 i + 5$$) $$-6$$
$$97$$ 97.1 = ($$-4 i + 9$$) $$5$$
$$97$$ 97.2 = ($$4 i + 9$$) $$5$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$1$$
$$9$$ 9.1 = ($$3$$) $$1$$