# Properties

 Base field $$\Q(\sqrt{-11})$$ Weight 2 Level norm 3136 Level $$\left(56\right)$$ Label 2.0.11.1-3136.1-a Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Related objects

## Base Field: $$\Q(\sqrt{-11})$$

Generator $$a$$, with minimal polynomial $$x^2 - x + 3$$; class number $$1$$.

## Form

 Weight 2 Level 3136.1 = $$\left(56\right)$$ Label 2.0.11.1-3136.1-a Dimension: 1 CM: no Base change: yes 56.2.a.a , 6776.2.a.g Newspace: 2.0.11.1-3136.1 (dimension 2) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a$$) $$0$$
$$3$$ 3.2 = ($$a - 1$$) $$0$$
$$4$$ 4.1 = ($$2$$) $$0$$
$$5$$ 5.1 = ($$-a - 1$$) $$2$$
$$5$$ 5.2 = ($$a - 2$$) $$2$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$-4$$
$$23$$ 23.1 = ($$a + 4$$) $$0$$
$$23$$ 23.2 = ($$a - 5$$) $$0$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$8$$
$$31$$ 31.2 = ($$3 a + 1$$) $$8$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$-2$$
$$37$$ 37.2 = ($$3 a - 5$$) $$-2$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$-8$$
$$47$$ 47.2 = ($$2 a + 5$$) $$-8$$
$$49$$ 49.1 = ($$7$$) $$1$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$6$$
$$53$$ 53.2 = ($$4 a + 1$$) $$6$$
$$59$$ 59.1 = ($$a + 7$$) $$0$$
$$59$$ 59.2 = ($$a - 8$$) $$0$$
$$67$$ 67.1 = ($$-3 a - 5$$) $$-4$$
$$67$$ 67.2 = ($$3 a - 8$$) $$-4$$
$$71$$ 71.1 = ($$-5 a + 1$$) $$-8$$
$$71$$ 71.2 = ($$5 a - 4$$) $$-8$$
$$89$$ 89.1 = ($$5 a + 2$$) $$-6$$
$$89$$ 89.2 = ($$5 a - 7$$) $$-6$$
$$97$$ 97.1 = ($$-3 a + 10$$) $$-6$$
$$97$$ 97.2 = ($$3 a + 7$$) $$-6$$
$$103$$ 103.1 = ($$-6 a + 1$$) $$-16$$
$$103$$ 103.2 = ($$6 a - 5$$) $$-16$$
$$113$$ 113.1 = ($$a + 10$$) $$2$$
$$113$$ 113.2 = ($$a - 11$$) $$2$$
$$137$$ 137.1 = ($$7 a - 5$$) $$-6$$
$$137$$ 137.2 = ($$7 a - 2$$) $$-6$$
$$157$$ 157.1 = ($$-3 a + 13$$) $$18$$
$$157$$ 157.2 = ($$3 a + 10$$) $$18$$
$$163$$ 163.1 = ($$-6 a - 5$$) $$-12$$
$$163$$ 163.2 = ($$6 a - 11$$) $$-12$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$-5 a + 13$$) $$-4$$
$$179$$ 179.2 = ($$-5 a - 8$$) $$-4$$
$$181$$ 181.1 = ($$-3 a - 11$$) $$10$$
$$181$$ 181.2 = ($$3 a - 14$$) $$10$$
$$191$$ 191.1 = ($$-7 a + 11$$) $$-16$$
$$191$$ 191.2 = ($$-7 a - 4$$) $$-16$$
$$199$$ 199.1 = ($$-6 a + 13$$) $$0$$
$$199$$ 199.2 = ($$6 a + 7$$) $$0$$
$$223$$ 223.1 = ($$-9 a + 5$$) $$0$$
$$223$$ 223.2 = ($$-9 a + 4$$) $$0$$
$$229$$ 229.1 = ($$9 a - 7$$) $$10$$
$$229$$ 229.2 = ($$9 a - 2$$) $$10$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$4$$ 4.1 = ($$2$$) $$-1$$
$$49$$ 49.1 = ($$7$$) $$-1$$