Base field 4.4.13888.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7,7,w - 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - 6x - 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ | $\phantom{-}e$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ | $-e^{2} + e + 8$ |
7 | $[7, 7, w - 2]$ | $-e^{2} + 7$ |
7 | $[7, 7, w - 1]$ | $-1$ |
9 | $[9, 3, w]$ | $\phantom{-}2e^{2} + e - 9$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ | $-e^{2} - e + 6$ |
23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ | $\phantom{-}2e^{2} - e - 11$ |
23 | $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ | $-e^{2} + e + 6$ |
31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ | $-2e^{2} - e + 5$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ | $\phantom{-}3e^{2} + e - 12$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ | $-2e^{2} + 4$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ | $-2e^{2} + 12$ |
47 | $[47, 47, w^{2} - w - 4]$ | $\phantom{-}4e^{2} - 20$ |
73 | $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ | $-3e^{2} - 5e + 14$ |
73 | $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ | $\phantom{-}6$ |
73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-2e^{2} - 3e + 5$ |
73 | $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ | $-3e - 1$ |
79 | $[79, 79, w^{2} - 5]$ | $-e^{2} - 2e - 3$ |
79 | $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ | $\phantom{-}e^{2} - 3e - 4$ |
97 | $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ | $\phantom{-}4e^{2} - 2e - 26$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,w - 1]$ | $1$ |