Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[27, 3, 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 3x^{2} - 13x + 23\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
8 | $[8, 2, 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w]$ | $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$ |
11 | $[11, 11, -w^{2} + 3w + 7]$ | $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$ |
11 | $[11, 11, w^{2} - 2w - 8]$ | $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$ |
23 | $[23, 23, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
23 | $[23, 23, w^{2} - 3w - 8]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
23 | $[23, 23, w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
27 | $[27, 3, 3]$ | $-1$ |
29 | $[29, 29, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$ |
29 | $[29, 29, w^{2} - 3w - 10]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$ |
29 | $[29, 29, w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$ |
31 | $[31, 31, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
31 | $[31, 31, -w^{2} + 3w + 9]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
31 | $[31, 31, w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
37 | $[37, 37, -w^{2} + 4w + 7]$ | $-3e + 2$ |
43 | $[43, 43, 2w^{2} - 6w - 13]$ | $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$ |
43 | $[43, 43, 2w^{2} - 4w - 17]$ | $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$ |
43 | $[43, 43, w^{2} - 2w - 12]$ | $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$ |
47 | $[47, 47, w^{2} - 4w - 4]$ | $-\frac{5}{4}e^{2} + 3e + \frac{41}{4}$ |
47 | $[47, 47, w^{2} - w - 5]$ | $-\frac{5}{4}e^{2} + 3e + \frac{41}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$27$ | $[27, 3, 3]$ | $1$ |