# Properties

 Base field $\Q(\sqrt{-3})$ Weight 2 Level norm 343 Level $\left(21 a - 14\right)$ Label 2.0.3.1-343.3-a Dimension 1 CM no Base-change no Sign +1 Analytic rank $0$

# Related objects

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

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

## Form

 Weight 2 Level 343.3 = $\left(21 a - 14\right)$ Label 2.0.3.1-343.3-a Dimension: 1 CM: no Base change: no, but is a twist of the base-change of a form over $\mathbb{Q}$ with coefficients in $\mathbb{Q}(\sqrt{3})$ Newspace: 2.0.3.1-343.3 (dimension 1) Sign of functional equation: +1 Analytic rank: $0$ L-ratio: 1

## Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

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

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ 7.1 = ($-3 a + 1$) $1$
$7$ 7.2 = ($3 a - 2$) $-1$