Base field 4.4.12357.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}0$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{1}{2}e - 3$ |
16 | $[16, 2, 2]$ | $\phantom{-}e + 3$ |
17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{1}{2}e - 3$ |
19 | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $-1$ |
23 | $[23, 23, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{3}{2}e + 3$ |
31 | $[31, 31, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}2e$ |
41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{3}{2}e + 3$ |
43 | $[43, 43, w^{3} + w^{2} - 5w - 4]$ | $-8$ |
53 | $[53, 53, w^{3} - w^{2} - 4w - 1]$ | $-2e$ |
53 | $[53, 53, -w^{2} - w + 4]$ | $\phantom{-}12$ |
59 | $[59, 59, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{7}{2}e - 3$ |
67 | $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ | $\phantom{-}3e - 4$ |
89 | $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ | $-12$ |
89 | $[89, 89, w^{3} - 5w + 1]$ | $-2e$ |
97 | $[97, 97, w^{3} - 6w - 1]$ | $\phantom{-}6$ |
97 | $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ | $-6$ |
101 | $[101, 101, -w^{3} + 6w - 2]$ | $\phantom{-}3e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $1$ |