# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 3249 Level $$\left(57\right)$$ Label 2.0.7.1-3249.1-a Dimension 1 CM no Base-change yes Sign -1 Analytic rank odd

# Related objects

## Base field: $$\Q(\sqrt{-7})$$

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

## Form

 Weight 2 Level 3249.1 = $$\left(57\right)$$ Label 2.0.7.1-3249.1-a Dimension: 1 CM: no Base change: yes 2793.2.a.b , 57.2.a.a Newspace: 2.0.7.1-3249.1 (dimension 3) Sign of functional equation: -1 Analytic rank: odd

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$9$$ 9.1 = ($$3$$) $$-1$$
$$361$$ 361.1 = ($$19$$) $$-1$$

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 eigenvalues of which we only show 50. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$2$$ 2.1 = ($$a$$) $$-2$$
$$2$$ 2.2 = ($$-a + 1$$) $$-2$$
$$7$$ 7.1 = ($$-2 a + 1$$) $$-5$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$1$$
$$11$$ 11.2 = ($$2 a + 1$$) $$1$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$-4$$
$$23$$ 23.2 = ($$2 a + 3$$) $$-4$$
$$25$$ 25.1 = ($$5$$) $$-1$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$-2$$
$$29$$ 29.2 = ($$4 a - 3$$) $$-2$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$0$$
$$37$$ 37.2 = ($$4 a + 1$$) $$0$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$-1$$
$$43$$ 43.2 = ($$2 a + 5$$) $$-1$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$10$$
$$53$$ 53.2 = ($$4 a - 7$$) $$10$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$8$$
$$67$$ 67.2 = ($$6 a - 5$$) $$8$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-12$$
$$71$$ 71.2 = ($$2 a + 7$$) $$-12$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$16$$
$$79$$ 79.2 = ($$6 a + 1$$) $$16$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$6$$
$$107$$ 107.2 = ($$2 a + 9$$) $$6$$
$$109$$ 109.1 = ($$-4 a - 7$$) $$4$$
$$109$$ 109.2 = ($$4 a - 11$$) $$4$$
$$113$$ 113.1 = ($$-8 a + 3$$) $$2$$
$$113$$ 113.2 = ($$-8 a + 5$$) $$2$$
$$127$$ 127.1 = ($$-6 a - 5$$) $$-2$$
$$127$$ 127.2 = ($$6 a - 11$$) $$-2$$
$$137$$ 137.1 = ($$-8 a + 9$$) $$-9$$
$$137$$ 137.2 = ($$8 a + 1$$) $$-9$$
$$149$$ 149.1 = ($$-4 a + 13$$) $$-21$$
$$149$$ 149.2 = ($$4 a + 9$$) $$-21$$
$$151$$ 151.1 = ($$-2 a + 13$$) $$0$$
$$151$$ 151.2 = ($$2 a + 11$$) $$0$$
$$163$$ 163.1 = ($$-6 a + 13$$) $$0$$
$$163$$ 163.2 = ($$6 a + 7$$) $$0$$
$$169$$ 169.1 = ($$13$$) $$-22$$
$$179$$ 179.1 = ($$10 a - 7$$) $$-18$$
$$179$$ 179.2 = ($$10 a - 3$$) $$-18$$
$$191$$ 191.1 = ($$-10 a + 1$$) $$9$$
$$191$$ 191.2 = ($$10 a - 9$$) $$9$$
$$193$$ 193.1 = ($$-8 a - 5$$) $$4$$
$$193$$ 193.2 = ($$-8 a + 13$$) $$4$$
$$197$$ 197.1 = ($$-4 a - 11$$) $$-2$$
$$197$$ 197.2 = ($$4 a - 15$$) $$-2$$
$$211$$ 211.1 = ($$-10 a + 11$$) $$12$$
$$211$$ 211.2 = ($$10 a + 1$$) $$12$$
$$233$$ 233.1 = ($$-8 a - 7$$) $$9$$
$$233$$ 233.2 = ($$8 a - 15$$) $$9$$