Base field 4.4.1957.1
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[71, 71, 2w^{2} - w - 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 4x^{2} - 12x + 36\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 3w + 1]$ | $\phantom{-}2$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{3}e^{2} - \frac{2}{3}e + 7$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{2}{3}e - 6$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 2]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}e - 4$ |
27 | $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ | $-\frac{2}{3}e^{2} - \frac{1}{3}e + 10$ |
31 | $[31, 31, -w^{3} + 5w]$ | $-4$ |
37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{4}{3}e^{2} - \frac{7}{3}e - 12$ |
43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{4}{3}e^{2} + \frac{7}{3}e + 12$ |
43 | $[43, 43, -w^{2} + 2w + 3]$ | $-\frac{1}{3}e^{2} - \frac{2}{3}e + 4$ |
47 | $[47, 47, -w^{3} + w^{2} + 2w + 2]$ | $-\frac{2}{3}e^{2} + \frac{5}{3}e + 6$ |
47 | $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{2}{3}e$ |
53 | $[53, 53, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{4}{3}e^{2} + \frac{4}{3}e + 14$ |
59 | $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{11}{3}e - 4$ |
59 | $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{4}{3}e - 12$ |
61 | $[61, 61, -w^{3} + w^{2} + w - 2]$ | $-2e + 6$ |
67 | $[67, 67, 2w^{3} - 5w - 2]$ | $-\frac{4}{3}e^{2} + \frac{4}{3}e + 16$ |
71 | $[71, 71, 2w^{2} - w - 3]$ | $-1$ |
73 | $[73, 73, 2w^{2} - w - 5]$ | $-\frac{2}{3}e^{2} + \frac{8}{3}e + 6$ |
73 | $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ | $-\frac{2}{3}e^{2} + \frac{5}{3}e + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$71$ | $[71, 71, 2w^{2} - w - 3]$ | $1$ |