# Properties

 Base field $$\Q(\sqrt{-11})$$ Weight 2 Level norm 2809 Level $$\left(53\right)$$ Label 2.0.11.1-2809.2-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 2809.2 = $$\left(53\right)$$ Label 2.0.11.1-2809.2-a Dimension: 1 CM: no Base change: yes 53.2.a.a , 6413.2.a.h Newspace: 2.0.11.1-2809.2 (dimension 4) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a$$) $$-3$$
$$3$$ 3.2 = ($$a - 1$$) $$-3$$
$$4$$ 4.1 = ($$2$$) $$-3$$
$$5$$ 5.1 = ($$-a - 1$$) $$0$$
$$5$$ 5.2 = ($$a - 2$$) $$0$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$0$$
$$23$$ 23.1 = ($$a + 4$$) $$7$$
$$23$$ 23.2 = ($$a - 5$$) $$7$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$4$$
$$31$$ 31.2 = ($$3 a + 1$$) $$4$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$5$$
$$37$$ 37.2 = ($$3 a - 5$$) $$5$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$-2$$
$$47$$ 47.2 = ($$2 a + 5$$) $$-2$$
$$49$$ 49.1 = ($$7$$) $$2$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$-1$$
$$53$$ 53.2 = ($$4 a + 1$$) $$-1$$
$$59$$ 59.1 = ($$a + 7$$) $$-2$$
$$59$$ 59.2 = ($$a - 8$$) $$-2$$
$$67$$ 67.1 = ($$-3 a - 5$$) $$-12$$
$$67$$ 67.2 = ($$3 a - 8$$) $$-12$$
$$71$$ 71.1 = ($$-5 a + 1$$) $$1$$
$$71$$ 71.2 = ($$5 a - 4$$) $$1$$
$$89$$ 89.1 = ($$5 a + 2$$) $$-14$$
$$89$$ 89.2 = ($$5 a - 7$$) $$-14$$
$$97$$ 97.1 = ($$-3 a + 10$$) $$1$$
$$97$$ 97.2 = ($$3 a + 7$$) $$1$$
$$103$$ 103.1 = ($$-6 a + 1$$) $$-1$$
$$103$$ 103.2 = ($$6 a - 5$$) $$-1$$
$$113$$ 113.1 = ($$a + 10$$) $$15$$
$$113$$ 113.2 = ($$a - 11$$) $$15$$
$$137$$ 137.1 = ($$7 a - 5$$) $$12$$
$$137$$ 137.2 = ($$7 a - 2$$) $$12$$
$$157$$ 157.1 = ($$-3 a + 13$$) $$-4$$
$$157$$ 157.2 = ($$3 a + 10$$) $$-4$$
$$163$$ 163.1 = ($$-6 a - 5$$) $$-6$$
$$163$$ 163.2 = ($$6 a - 11$$) $$-6$$
$$169$$ 169.1 = ($$13$$) $$-17$$
$$179$$ 179.1 = ($$-5 a + 13$$) $$11$$
$$179$$ 179.2 = ($$-5 a - 8$$) $$11$$
$$181$$ 181.1 = ($$-3 a - 11$$) $$-2$$
$$181$$ 181.2 = ($$3 a - 14$$) $$-2$$
$$191$$ 191.1 = ($$-7 a + 11$$) $$-21$$
$$191$$ 191.2 = ($$-7 a - 4$$) $$-21$$
$$199$$ 199.1 = ($$-6 a + 13$$) $$4$$
$$199$$ 199.2 = ($$6 a + 7$$) $$4$$
$$223$$ 223.1 = ($$-9 a + 5$$) $$-14$$
$$223$$ 223.2 = ($$-9 a + 4$$) $$-14$$
$$229$$ 229.1 = ($$9 a - 7$$) $$21$$
$$229$$ 229.2 = ($$9 a - 2$$) $$21$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$53$$ 53.1 = ($$-4 a + 5$$) $$1$$
$$53$$ 53.2 = ($$4 a + 1$$) $$1$$