# Properties

 Base field $\Q(\sqrt{-1})$ Weight 2 Level norm 16384 Level $\left(128\right)$ Label 2.0.4.1-16384.1-d Dimension 1 CM no Base-change yes Sign +1 Analytic rank $0$

# Related objects

## Base Field: $\Q(\sqrt{-1})$

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

## Form

 Weight 2 Level 16384.1 = $\left(128\right)$ Label 2.0.4.1-16384.1-d Dimension: 1 CM: no Base change: yes, of a form over $\mathbb{Q}$ with coefficients in $\mathbb{Q}(\sqrt{2})$ Newspace: 2.0.4.1-16384.1 (dimension 14) Sign of functional equation: +1 Analytic rank: $0$ L-ratio: 1

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$2$ 2.1 = ($i + 1$) $0$
$5$ 5.1 = ($-i - 2$) $2$
$5$ 5.2 = ($2 i + 1$) $2$
$9$ 9.1 = ($3$) $-4$
$13$ 13.1 = ($-3 i - 2$) $6$
$13$ 13.2 = ($2 i + 3$) $6$
$17$ 17.1 = ($i + 4$) $0$
$17$ 17.2 = ($i - 4$) $0$
$29$ 29.1 = ($-2 i + 5$) $2$
$29$ 29.2 = ($2 i + 5$) $2$
$37$ 37.1 = ($i + 6$) $6$
$37$ 37.2 = ($i - 6$) $6$
$41$ 41.1 = ($-5 i - 4$) $6$
$41$ 41.2 = ($4 i + 5$) $6$
$49$ 49.1 = ($7$) $-6$
$53$ 53.1 = ($-2 i + 7$) $-2$
$53$ 53.2 = ($2 i + 7$) $-2$
$61$ 61.1 = ($-6 i - 5$) $6$
$61$ 61.2 = ($5 i + 6$) $6$
$73$ 73.1 = ($-3 i - 8$) $-12$
$73$ 73.2 = ($3 i - 8$) $-12$
$89$ 89.1 = ($-5 i + 8$) $-12$
$89$ 89.2 = ($-8 i + 5$) $-12$
$97$ 97.1 = ($-4 i + 9$) $-8$
$97$ 97.2 = ($4 i + 9$) $-8$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ 2.1 = ($i + 1$) $-1$