Properties

 Base field $$\Q(\sqrt{-11})$$ Weight 2 Level norm 207 Level $$\left(-2 a + 15\right)$$ Label 2.0.11.1-207.1-b Dimension 1 CM no Base-change no 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 207.1 = $$\left(-2 a + 15\right)$$ Label 2.0.11.1-207.1-b Dimension: 1 CM: no Base change: no Newspace: 2.0.11.1-207.1 (dimension 2) Sign of functional equation: -1 Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$$3$$ 3.1 = ($$-a$$) $$-1$$
$$23$$ 23.1 = ($$a + 4$$) $$-1$$

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 1000 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
$$3$$ 3.2 = ($$a - 1$$) $$1$$
$$4$$ 4.1 = ($$2$$) $$1$$
$$5$$ 5.1 = ($$-a - 1$$) $$-2$$
$$5$$ 5.2 = ($$a - 2$$) $$-3$$
$$11$$ 11.1 = ($$-2 a + 1$$) $$-5$$
$$23$$ 23.2 = ($$a - 5$$) $$6$$
$$31$$ 31.1 = ($$-3 a + 4$$) $$-5$$
$$31$$ 31.2 = ($$3 a + 1$$) $$0$$
$$37$$ 37.1 = ($$-3 a - 2$$) $$3$$
$$37$$ 37.2 = ($$3 a - 5$$) $$-2$$
$$47$$ 47.1 = ($$-2 a + 7$$) $$-3$$
$$47$$ 47.2 = ($$2 a + 5$$) $$-12$$
$$49$$ 49.1 = ($$7$$) $$9$$
$$53$$ 53.1 = ($$-4 a + 5$$) $$4$$
$$53$$ 53.2 = ($$4 a + 1$$) $$-9$$
$$59$$ 59.1 = ($$a + 7$$) $$-5$$
$$59$$ 59.2 = ($$a - 8$$) $$10$$
$$67$$ 67.1 = ($$-3 a - 5$$) $$-8$$
$$67$$ 67.2 = ($$3 a - 8$$) $$2$$
$$71$$ 71.1 = ($$-5 a + 1$$) $$7$$
$$71$$ 71.2 = ($$5 a - 4$$) $$-12$$
$$89$$ 89.1 = ($$5 a + 2$$) $$6$$
$$89$$ 89.2 = ($$5 a - 7$$) $$14$$
$$97$$ 97.1 = ($$-3 a + 10$$) $$-3$$
$$97$$ 97.2 = ($$3 a + 7$$) $$12$$
$$103$$ 103.1 = ($$-6 a + 1$$) $$1$$
$$103$$ 103.2 = ($$6 a - 5$$) $$-19$$
$$113$$ 113.1 = ($$a + 10$$) $$-4$$
$$113$$ 113.2 = ($$a - 11$$) $$19$$
$$137$$ 137.1 = ($$7 a - 5$$) $$-8$$
$$137$$ 137.2 = ($$7 a - 2$$) $$3$$
$$157$$ 157.1 = ($$-3 a + 13$$) $$-7$$
$$157$$ 157.2 = ($$3 a + 10$$) $$-2$$
$$163$$ 163.1 = ($$-6 a - 5$$) $$4$$
$$163$$ 163.2 = ($$6 a - 11$$) $$-6$$
$$169$$ 169.1 = ($$13$$) $$1$$
$$179$$ 179.1 = ($$-5 a + 13$$) $$-4$$
$$179$$ 179.2 = ($$-5 a - 8$$) $$4$$
$$181$$ 181.1 = ($$-3 a - 11$$) $$5$$
$$181$$ 181.2 = ($$3 a - 14$$) $$0$$
$$191$$ 191.1 = ($$-7 a + 11$$) $$0$$
$$191$$ 191.2 = ($$-7 a - 4$$) $$-20$$
$$199$$ 199.1 = ($$-6 a + 13$$) $$-10$$
$$199$$ 199.2 = ($$6 a + 7$$) $$-20$$
$$223$$ 223.1 = ($$-9 a + 5$$) $$4$$
$$223$$ 223.2 = ($$-9 a + 4$$) $$-11$$
$$229$$ 229.1 = ($$9 a - 7$$) $$-10$$
$$229$$ 229.2 = ($$9 a - 2$$) $$20$$
$$251$$ 251.1 = ($$-5 a + 16$$) $$-18$$
$$251$$ 251.2 = ($$5 a + 11$$) $$-22$$