# 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 $0$

# Related objects

## 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 = ($5$) $1$