Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[4, 2, -w^{2} + 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 14x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
5 | $[5, 5, w]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{2} + 6]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $-\frac{1}{3}e^{2} + \frac{10}{3}$ |
7 | $[7, 7, w + 2]$ | $-\frac{1}{3}e^{3} + \frac{16}{3}e$ |
11 | $[11, 11, 2w - 1]$ | $-\frac{2}{3}e^{3} + \frac{26}{3}e$ |
13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{29}{3}e$ |
27 | $[27, 3, 3]$ | $-\frac{2}{3}e^{2} + \frac{8}{3}$ |
41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{55}{3}e$ |
41 | $[41, 41, 3w^{2} - w - 23]$ | $-e^{2} + 2$ |
41 | $[41, 41, w^{2} - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{19}{3}e$ |
43 | $[43, 43, w^{2} - w - 3]$ | $\phantom{-}2e$ |
47 | $[47, 47, -w - 4]$ | $-\frac{4}{3}e^{2} + \frac{28}{3}$ |
49 | $[49, 7, 3w^{2} - 2w - 24]$ | $\phantom{-}\frac{5}{3}e^{3} - \frac{59}{3}e$ |
53 | $[53, 53, 2w^{2} - w - 12]$ | $-\frac{1}{3}e^{3} + \frac{19}{3}e$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{10}{3}e$ |
61 | $[61, 61, -w^{2} + 3w - 3]$ | $-\frac{5}{3}e^{2} + \frac{26}{3}$ |
71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}12$ |
79 | $[79, 79, 2w + 3]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{64}{3}e$ |
89 | $[89, 89, 2w - 7]$ | $\phantom{-}e^{2} - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 1]$ | $-1$ |