# Properties

 Base field $\Q(\sqrt{-1})$ Weight 2 Level norm 100 Level $\left(10\right)$ Label 2.0.4.1-100.2-a 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 100.2 = $\left(10\right)$ Label 2.0.4.1-100.2-a Dimension: 1 CM: no Base change: yes 80.2.1.b , 20.2.1.a Newspace: 2.0.4.1-100.2 (dimension 1) Sign of functional equation: +1 Analytic rank: $0$ L-ratio: 1/2

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$2$ 2.1 = ($i + 1$) $0$
$5$ 5.1 = ($-i - 2$) $-1$
$5$ 5.2 = ($2 i + 1$) $-1$
$9$ 9.1 = ($3$) $-2$
$13$ 13.1 = ($-3 i - 2$) $2$
$13$ 13.2 = ($2 i + 3$) $2$
$17$ 17.1 = ($i + 4$) $-6$
$17$ 17.2 = ($i - 4$) $-6$
$29$ 29.1 = ($-2 i + 5$) $6$
$29$ 29.2 = ($2 i + 5$) $6$
$37$ 37.1 = ($i + 6$) $2$
$37$ 37.2 = ($i - 6$) $2$
$41$ 41.1 = ($-5 i - 4$) $6$
$41$ 41.2 = ($4 i + 5$) $6$
$49$ 49.1 = ($7$) $-10$
$53$ 53.1 = ($-2 i + 7$) $-6$
$53$ 53.2 = ($2 i + 7$) $-6$
$61$ 61.1 = ($-6 i - 5$) $2$
$61$ 61.2 = ($5 i + 6$) $2$
$73$ 73.1 = ($-3 i - 8$) $2$
$73$ 73.2 = ($3 i - 8$) $2$
$89$ 89.1 = ($-5 i + 8$) $-6$
$89$ 89.2 = ($-8 i + 5$) $-6$
$97$ 97.1 = ($-4 i + 9$) $2$
$97$ 97.2 = ($4 i + 9$) $2$
$101$ 101.1 = ($i + 10$) $6$
$101$ 101.2 = ($i - 10$) $6$
$109$ 109.1 = ($-3 i + 10$) $2$
$109$ 109.2 = ($3 i + 10$) $2$
$113$ 113.1 = ($-8 i - 7$) $-6$
$113$ 113.2 = ($7 i + 8$) $-6$
$121$ 121.1 = ($11$) $-22$
$137$ 137.1 = ($-4 i - 11$) $18$
$137$ 137.2 = ($4 i - 11$) $18$
$149$ 149.1 = ($10 i - 7$) $-6$
$149$ 149.2 = ($7 i - 10$) $-6$
$157$ 157.1 = ($-6 i - 11$) $-22$
$157$ 157.2 = ($6 i - 11$) $-22$
$173$ 173.1 = ($-2 i + 13$) $-6$
$173$ 173.2 = ($2 i + 13$) $-6$
$181$ 181.1 = ($-10 i - 9$) $-10$
$181$ 181.2 = ($9 i + 10$) $-10$
$193$ 193.1 = ($7 i - 12$) $26$
$193$ 193.2 = ($7 i + 12$) $26$
$197$ 197.1 = ($i + 14$) $18$
$197$ 197.2 = ($i - 14$) $18$
$229$ 229.1 = ($-2 i + 15$) $14$
$229$ 229.2 = ($2 i + 15$) $14$
$233$ 233.1 = ($-8 i - 13$) $-6$
$233$ 233.2 = ($-8 i + 13$) $-6$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ 2.1 = ($i + 1$) $-1$
$5$ 5.1 = ($-i - 2$) $1$
$5$ 5.2 = ($2 i + 1$) $1$