Base field 3.3.993.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[21, 21, w^{2} - 2w - 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 3x^{2} - 9x + 13\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w]$ | $-1$ |
3 | $[3, 3, w - 1]$ | $-1$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 1]$ | $-1$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{5}{3}$ |
13 | $[13, 13, w^{2} - w - 4]$ | $-\frac{1}{3}e^{2} - \frac{2}{3}e + \frac{11}{3}$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}e - \frac{5}{3}$ |
25 | $[25, 5, -w^{2} - w + 4]$ | $-\frac{2}{3}e^{2} + \frac{2}{3}e + \frac{10}{3}$ |
31 | $[31, 31, w^{2} - w - 1]$ | $-e^{2} + e + 5$ |
31 | $[31, 31, 2w^{2} - w - 14]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{5}{3}e - \frac{10}{3}$ |
31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{8}{3}e - \frac{13}{3}$ |
37 | $[37, 37, -3w^{2} + w + 19]$ | $-8$ |
49 | $[49, 7, w^{2} - 2w - 4]$ | $-e^{2} + 2e + 5$ |
53 | $[53, 53, -w - 4]$ | $-\frac{4}{3}e^{2} + \frac{4}{3}e + \frac{29}{3}$ |
61 | $[61, 61, 2w^{2} + w - 7]$ | $-\frac{2}{3}e^{2} + \frac{5}{3}e + \frac{4}{3}$ |
71 | $[71, 71, 2w^{2} - 2w - 13]$ | $-2e - 2$ |
73 | $[73, 73, w - 5]$ | $-e^{2} + 3e + 5$ |
83 | $[83, 83, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}e - \frac{23}{3}$ |
89 | $[89, 89, w^{2} + 2w - 4]$ | $-\frac{2}{3}e^{2} + \frac{14}{3}e + \frac{16}{3}$ |
97 | $[97, 97, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{10}{3}e - \frac{28}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w]$ | $1$ |
$7$ | $[7, 7, w + 1]$ | $1$ |