# Properties

 Base field $$\Q(\sqrt{-1})$$ Weight 2 Level norm 338 Level $$\left(13 i + 13\right)$$ Label 2.0.4.1-338.2-a 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 338.2 = $$\left(13 i + 13\right)$$ Label 2.0.4.1-338.2-a Dimension: 1 CM: no Base change: yes 26.2.a.a , 208.2.a.a Newspace: 2.0.4.1-338.2 (dimension 2) 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 = ($$-i - 2$$) $$-3$$
$$5$$ 5.2 = ($$2 i + 1$$) $$-3$$
$$9$$ 9.1 = ($$3$$) $$-5$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$1$$
$$13$$ 13.2 = ($$2 i + 3$$) $$1$$
$$17$$ 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 = ($$i + 6$$) $$-7$$
$$37$$ 37.2 = ($$i - 6$$) $$-7$$
$$41$$ 41.1 = ($$-5 i - 4$$) $$0$$
$$41$$ 41.2 = ($$4 i + 5$$) $$0$$
$$49$$ 49.1 = ($$7$$) $$-13$$
$$53$$ 53.1 = ($$-2 i + 7$$) $$0$$
$$53$$ 53.2 = ($$2 i + 7$$) $$0$$
$$61$$ 61.1 = ($$-6 i - 5$$) $$8$$
$$61$$ 61.2 = ($$5 i + 6$$) $$8$$
$$73$$ 73.1 = ($$-3 i - 8$$) $$2$$
$$73$$ 73.2 = ($$3 i - 8$$) $$2$$
$$89$$ 89.1 = ($$-5 i + 8$$) $$-6$$
$$89$$ 89.2 = ($$-8 i + 5$$) $$-6$$
$$97$$ 97.1 = ($$-4 i + 9$$) $$-10$$
$$97$$ 97.2 = ($$4 i + 9$$) $$-10$$
$$101$$ 101.1 = ($$i + 10$$) $$-12$$
$$101$$ 101.2 = ($$i - 10$$) $$-12$$
$$109$$ 109.1 = ($$-3 i + 10$$) $$-7$$
$$109$$ 109.2 = ($$3 i + 10$$) $$-7$$
$$113$$ 113.1 = ($$-8 i - 7$$) $$-6$$
$$113$$ 113.2 = ($$7 i + 8$$) $$-6$$
$$121$$ 121.1 = ($$11$$) $$14$$
$$137$$ 137.1 = ($$-4 i - 11$$) $$0$$
$$137$$ 137.2 = ($$4 i - 11$$) $$0$$
$$149$$ 149.1 = ($$10 i - 7$$) $$-6$$
$$149$$ 149.2 = ($$7 i - 10$$) $$-6$$
$$157$$ 157.1 = ($$-6 i - 11$$) $$14$$
$$157$$ 157.2 = ($$6 i - 11$$) $$14$$
$$173$$ 173.1 = ($$-2 i + 13$$) $$0$$
$$173$$ 173.2 = ($$2 i + 13$$) $$0$$
$$181$$ 181.1 = ($$-10 i - 9$$) $$20$$
$$181$$ 181.2 = ($$9 i + 10$$) $$20$$
$$193$$ 193.1 = ($$7 i - 12$$) $$-4$$
$$193$$ 193.2 = ($$7 i + 12$$) $$-4$$
$$197$$ 197.1 = ($$i + 14$$) $$3$$
$$197$$ 197.2 = ($$i - 14$$) $$3$$
$$229$$ 229.1 = ($$-2 i + 15$$) $$-13$$
$$229$$ 229.2 = ($$2 i + 15$$) $$-13$$
$$233$$ 233.1 = ($$-8 i - 13$$) $$-27$$
$$233$$ 233.2 = ($$-8 i + 13$$) $$-27$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$i + 1$$) $$1$$
$$13$$ 13.1 = ($$-3 i - 2$$) $$-1$$
$$13$$ 13.2 = ($$2 i + 3$$) $$-1$$