Base field 4.4.17069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 2x^{3} - 8x^{2} - 12x + 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 3e - 2$ |
9 | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $-1$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{2}{3}e^{2} - 4e - 3$ |
17 | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $\phantom{-}e^{2} + e - 4$ |
17 | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 4e - 2$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 4$ |
17 | $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 4e + 4$ |
25 | $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ | $-e^{3} - e^{2} + 6e + 2$ |
25 | $[25, 5, w^{2} - 2w - 7]$ | $-e^{3} - e^{2} + 6e + 2$ |
29 | $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 4e$ |
29 | $[29, 29, w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 4e + 6$ |
53 | $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{1}{3}e^{2} - 12e - 2$ |
53 | $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ | $\phantom{-}e^{2} + 4e - 4$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 2e + 4$ |
61 | $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 2e + 4$ |
101 | $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ | $-\frac{2}{3}e^{3} - \frac{2}{3}e^{2} + 4e + 6$ |
103 | $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{5}{3}e^{3} + \frac{11}{3}e^{2} - 14e - 14$ |
103 | $[103, 103, -w^{3} + w^{2} + 8w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{5}{3}e^{2} + 2e + 14$ |
113 | $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{4}{3}e^{2} - 11e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $1$ |