Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[5, 5, -w - 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 4x^{2} - 3x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w - 1]$ | $-1$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 3]$ | $-\frac{1}{3}e^{2} - \frac{1}{3}e + 3$ |
7 | $[7, 7, -w + 2]$ | $-\frac{1}{3}e^{2} - \frac{4}{3}e$ |
7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - 1$ |
8 | $[8, 2, 2]$ | $\phantom{-}0$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{4}{3}e - 4$ |
19 | $[19, 19, -w^{2} + 5]$ | $-\frac{1}{3}e^{2} - \frac{7}{3}e - 3$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $-e - 3$ |
27 | $[27, 3, 3]$ | $\phantom{-}e^{2} + 3e - 2$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}e^{2} + e - 9$ |
31 | $[31, 31, w^{2} - w - 8]$ | $-\frac{2}{3}e^{2} - \frac{5}{3}e + 2$ |
37 | $[37, 37, -w - 4]$ | $-\frac{2}{3}e^{2} - \frac{2}{3}e + 5$ |
43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{4}{3}e^{2} - \frac{13}{3}e$ |
47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{2} + 5e - 6$ |
53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}e + 3$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $-2e^{2} - 7e + 3$ |
67 | $[67, 67, w^{2} + w - 8]$ | $-e^{2} - 6e + 5$ |
71 | $[71, 71, w^{2} + w - 11]$ | $-e^{2} + 9$ |
73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{5}{3}e^{2} + \frac{5}{3}e - 9$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w - 1]$ | $1$ |