# Properties

 Base field $\Q(\sqrt{-2})$ Weight 2 Level norm 256 Level $\left(16\right)$ Label 2.0.8.1-256.1-b Dimension 1 CM no Base-change yes Sign +1 Analytic rank $0$

# Related objects

## Base Field: $\Q(\sqrt{-2})$

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

## Form

 Weight 2 Level 256.1 = $\left(16\right)$ Label 2.0.8.1-256.1-b Dimension: 1 CM: no Base change: yes 128.2.1.d , 128.2.1.c Newspace: 2.0.8.1-256.1 (dimension 2) 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 = ($a$) $0$
$3$ 3.1 = ($-a - 1$) $2$
$3$ 3.2 = ($a - 1$) $2$
$11$ 11.1 = ($a + 3$) $-2$
$11$ 11.2 = ($a - 3$) $-2$
$17$ 17.1 = ($-2 a + 3$) $-2$
$17$ 17.2 = ($2 a + 3$) $-2$
$19$ 19.1 = ($-3 a + 1$) $2$
$19$ 19.2 = ($3 a + 1$) $2$
$25$ 25.1 = ($5$) $-6$
$41$ 41.1 = ($-4 a - 3$) $-6$
$41$ 41.2 = ($4 a - 3$) $-6$
$43$ 43.1 = ($-3 a - 5$) $6$
$43$ 43.2 = ($3 a - 5$) $6$
$49$ 49.1 = ($7$) $2$
$59$ 59.1 = ($-5 a + 3$) $14$
$59$ 59.2 = ($-5 a - 3$) $14$
$67$ 67.1 = ($-3 a + 7$) $10$
$67$ 67.2 = ($3 a + 7$) $10$
$73$ 73.1 = ($-6 a + 1$) $14$
$73$ 73.2 = ($6 a + 1$) $14$
$83$ 83.1 = ($a + 9$) $-6$
$83$ 83.2 = ($a - 9$) $-6$
$89$ 89.1 = ($-2 a + 9$) $-2$
$89$ 89.2 = ($2 a + 9$) $-2$
$97$ 97.1 = ($-6 a - 5$) $-2$
$97$ 97.2 = ($6 a - 5$) $-2$
$107$ 107.1 = ($7 a + 3$) $-2$
$107$ 107.2 = ($7 a - 3$) $-2$
$113$ 113.1 = ($-4 a + 9$) $2$
$113$ 113.2 = ($4 a + 9$) $2$
$131$ 131.1 = ($-5 a - 9$) $-6$
$131$ 131.2 = ($5 a - 9$) $-6$
$137$ 137.1 = ($-8 a + 3$) $10$
$137$ 137.2 = ($-8 a - 3$) $10$
$139$ 139.1 = ($-3 a - 11$) $-10$
$139$ 139.2 = ($3 a - 11$) $-10$
$163$ 163.1 = ($-9 a + 1$) $2$
$163$ 163.2 = ($9 a + 1$) $2$
$169$ 169.1 = ($13$) $-22$
$179$ 179.1 = ($7 a + 9$) $-6$
$179$ 179.2 = ($7 a - 9$) $-6$
$193$ 193.1 = ($-6 a - 11$) $-2$
$193$ 193.2 = ($6 a - 11$) $-2$
$211$ 211.1 = ($9 a - 7$) $-22$
$211$ 211.2 = ($9 a + 7$) $-22$
$227$ 227.1 = ($a + 15$) $18$
$227$ 227.2 = ($a - 15$) $18$
$233$ 233.1 = ($-2 a + 15$) $-18$
$233$ 233.2 = ($2 a + 15$) $-18$

## Atkin-Lehner eigenvalues

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