# Properties

 Base field $\Q(\sqrt{-3})$ Weight 2 Level norm 412 Level $\left(22 a - 4\right)$ Label 2.0.3.1-412.2-a Dimension 1 CM no Base-change no Sign -1 Analytic rank odd

# Related objects

## Base Field: $\Q(\sqrt{-3})$

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

## Form

 Weight 2 Level 412.2 = $\left(22 a - 4\right)$ Label 2.0.3.1-412.2-a Dimension: 1 CM: no Base change: no Newspace: 2.0.3.1-412.2 (dimension 1) Sign of functional equation: -1 Analytic rank: odd

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
$3$ 3.1 = ($-2 a + 1$) $-3$
$4$ 4.1 = ($2$) $-1$
$7$ 7.1 = ($-3 a + 1$) $-4$
$7$ 7.2 = ($3 a - 2$) $-3$
$13$ 13.1 = ($-4 a + 1$) $1$
$13$ 13.2 = ($4 a - 3$) $-5$
$19$ 19.1 = ($-5 a + 3$) $0$
$19$ 19.2 = ($-5 a + 2$) $1$
$25$ 25.1 = ($5$) $-2$
$31$ 31.1 = ($-6 a + 1$) $2$
$31$ 31.2 = ($6 a - 5$) $-2$
$37$ 37.1 = ($-7 a + 4$) $1$
$37$ 37.2 = ($-7 a + 3$) $-4$
$43$ 43.1 = ($-7 a + 1$) $12$
$43$ 43.2 = ($7 a - 6$) $-11$
$61$ 61.1 = ($-9 a + 5$) $-12$
$61$ 61.2 = ($-9 a + 4$) $0$
$67$ 67.1 = ($9 a - 7$) $-2$
$67$ 67.2 = ($9 a - 2$) $4$
$73$ 73.1 = ($-9 a + 1$) $8$
$73$ 73.2 = ($9 a - 8$) $-14$
$79$ 79.1 = ($10 a - 7$) $5$
$79$ 79.2 = ($10 a - 3$) $-10$
$97$ 97.1 = ($-11 a + 3$) $-5$
$97$ 97.2 = ($-11 a + 8$) $-5$
$103$ 103.1 = ($11 a - 9$) $-4$
$103$ 103.2 = ($11 a - 2$) $-1$
$109$ 109.1 = ($12 a - 5$) $19$
$109$ 109.2 = ($-12 a + 7$) $-6$
$121$ 121.1 = ($11$) $-5$
$127$ 127.1 = ($-13 a + 7$) $-8$
$127$ 127.2 = ($-13 a + 6$) $7$
$139$ 139.1 = ($13 a - 10$) $9$
$139$ 139.2 = ($13 a - 3$) $-4$
$151$ 151.1 = ($-14 a + 5$) $-14$
$151$ 151.2 = ($-14 a + 9$) $-10$
$157$ 157.1 = ($-13 a + 1$) $8$
$157$ 157.2 = ($13 a - 12$) $1$
$163$ 163.1 = ($-14 a + 3$) $-12$
$163$ 163.2 = ($-14 a + 11$) $14$
$181$ 181.1 = ($-15 a + 4$) $-22$
$181$ 181.2 = ($-15 a + 11$) $-8$
$193$ 193.1 = ($16 a - 7$) $12$
$193$ 193.2 = ($-16 a + 9$) $21$
$199$ 199.1 = ($15 a - 13$) $-6$
$199$ 199.2 = ($15 a - 2$) $26$
$211$ 211.1 = ($-15 a + 1$) $2$
$211$ 211.2 = ($15 a - 14$) $22$
$223$ 223.1 = ($-17 a + 6$) $-8$
$223$ 223.2 = ($-17 a + 11$) $20$

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ 4.1 = ($2$) $1$
$103$ 103.2 = ($11 a - 2$) $1$