Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[17, 17, -w - 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 11x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $-2$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w + 2]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
8 | $[8, 2, 2]$ | $-1$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $-e$ |
17 | $[17, 17, -w - 3]$ | $-1$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$ |
17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}2e$ |
27 | $[27, 3, -3]$ | $\phantom{-}e^{2} - 4$ |
29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}0$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$ |
29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}e^{3} - 12e$ |
31 | $[31, 31, w^{2} - 2]$ | $-e$ |
37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{25}{2}e$ |
43 | $[43, 43, w^{2} - 2w - 5]$ | $\phantom{-}0$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-2e^{2} + 10$ |
49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e$ |
53 | $[53, 53, w^{2} - 2w - 6]$ | $-4$ |
71 | $[71, 71, w - 5]$ | $-2e^{2} + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w - 3]$ | $1$ |