# Properties

 Base field $$\Q(\sqrt{-7})$$ Weight 2 Level norm 10000 Level $$\left(-75 a + 50\right)$$ Label 2.0.7.1-10000.1-b Dimension 1 CM -35 Base-change no Sign +1 Analytic rank $$0$$

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

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

## Form

 Weight 2 Level 10000.1 = $$\left(-75 a + 50\right)$$ Label 2.0.7.1-10000.1-b Dimension: 1 CM: -35 Base change: no, but is a twist of the base-change of a form over $$\mathbb{Q}$$ with coefficients in $$\mathbb{Q}(\sqrt{5})$$ Newspace: 2.0.7.1-10000.1 (dimension 4) Sign of functional equation: +1 Analytic rank: $$0$$ L-ratio: 2

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$0$$
$$2$$ 2.2 = ($$-a + 1$$) $$0$$
$$7$$ 7.1 = ($$-2 a + 1$$) $$0$$
$$9$$ 9.1 = ($$3$$) $$-1$$
$$11$$ 11.1 = ($$-2 a + 3$$) $$3$$
$$11$$ 11.2 = ($$2 a + 1$$) $$-3$$
$$23$$ 23.1 = ($$-2 a + 5$$) $$0$$
$$23$$ 23.2 = ($$2 a + 3$$) $$0$$
$$25$$ 25.1 = ($$5$$) $$0$$
$$29$$ 29.1 = ($$-4 a + 1$$) $$9$$
$$29$$ 29.2 = ($$4 a - 3$$) $$9$$
$$37$$ 37.1 = ($$-4 a + 5$$) $$0$$
$$37$$ 37.2 = ($$4 a + 1$$) $$0$$
$$43$$ 43.1 = ($$-2 a + 7$$) $$0$$
$$43$$ 43.2 = ($$2 a + 5$$) $$0$$
$$53$$ 53.1 = ($$-4 a - 3$$) $$0$$
$$53$$ 53.2 = ($$4 a - 7$$) $$0$$
$$67$$ 67.1 = ($$-6 a + 1$$) $$0$$
$$67$$ 67.2 = ($$6 a - 5$$) $$0$$
$$71$$ 71.1 = ($$-2 a + 9$$) $$-12$$
$$71$$ 71.2 = ($$2 a + 7$$) $$12$$
$$79$$ 79.1 = ($$-6 a + 7$$) $$1$$
$$79$$ 79.2 = ($$6 a + 1$$) $$-1$$
$$107$$ 107.1 = ($$-2 a + 11$$) $$0$$
$$107$$ 107.2 = ($$2 a + 9$$) $$0$$
$$109$$ 109.1 = ($$-4 a - 7$$) $$11$$
$$109$$ 109.2 = ($$4 a - 11$$) $$11$$
$$113$$ 113.1 = ($$-8 a + 3$$) $$0$$
$$113$$ 113.2 = ($$-8 a + 5$$) $$0$$
$$127$$ 127.1 = ($$-6 a - 5$$) $$0$$
$$127$$ 127.2 = ($$6 a - 11$$) $$0$$
$$137$$ 137.1 = ($$-8 a + 9$$) $$0$$
$$137$$ 137.2 = ($$8 a + 1$$) $$0$$
$$149$$ 149.1 = ($$-4 a + 13$$) $$6$$
$$149$$ 149.2 = ($$4 a + 9$$) $$6$$
$$151$$ 151.1 = ($$-2 a + 13$$) $$17$$
$$151$$ 151.2 = ($$2 a + 11$$) $$-17$$
$$163$$ 163.1 = ($$-6 a + 13$$) $$0$$
$$163$$ 163.2 = ($$6 a + 7$$) $$0$$
$$169$$ 169.1 = ($$13$$) $$-19$$
$$179$$ 179.1 = ($$10 a - 7$$) $$-24$$
$$179$$ 179.2 = ($$10 a - 3$$) $$24$$
$$191$$ 191.1 = ($$-10 a + 1$$) $$27$$
$$191$$ 191.2 = ($$10 a - 9$$) $$-27$$
$$193$$ 193.1 = ($$-8 a - 5$$) $$0$$
$$193$$ 193.2 = ($$-8 a + 13$$) $$0$$
$$197$$ 197.1 = ($$-4 a - 11$$) $$0$$
$$197$$ 197.2 = ($$4 a - 15$$) $$0$$
$$211$$ 211.1 = ($$-10 a + 11$$) $$23$$
$$211$$ 211.2 = ($$10 a + 1$$) $$-23$$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$2$$ 2.1 = ($$a$$) $$-1$$
$$25$$ 25.1 = ($$5$$) $$1$$