Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 4, 3w^{2} - 4w - 22]$ |
Dimension: | $4$ |
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:
\(x^{4} + 2x^{3} - 5x^{2} - 10x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}0$ |
2 | $[2, 2, w^{2} - 2w - 5]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} + 3w + 1]$ | $\phantom{-}e^{3} + e^{2} - 5e - 4$ |
7 | $[7, 7, -2w^{2} + 2w + 17]$ | $-e^{2} + 3$ |
7 | $[7, 7, -w^{2} + w + 9]$ | $-e^{3} - e^{2} + 5e + 3$ |
13 | $[13, 13, 2w + 1]$ | $-e - 4$ |
25 | $[25, 5, -3w^{2} + 5w + 19]$ | $-2e^{3} - e^{2} + 12e + 8$ |
27 | $[27, 3, 3]$ | $\phantom{-}e^{2} - 1$ |
29 | $[29, 29, w^{2} + w - 1]$ | $-4e - 1$ |
31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}e^{3} - 7e$ |
37 | $[37, 37, 2w^{2} + 6w + 3]$ | $-e^{3} + 8e + 4$ |
41 | $[41, 41, -6w^{2} - 14w - 3]$ | $\phantom{-}e^{3} + e^{2} - 7e - 7$ |
53 | $[53, 53, -4w^{2} + 6w + 27]$ | $-e^{2} + e + 1$ |
59 | $[59, 59, 2w^{2} - 4w - 11]$ | $\phantom{-}e^{3} - e^{2} - 5e - 1$ |
61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}2e^{3} + 2e^{2} - 10e - 11$ |
61 | $[61, 61, -2w^{2} + 2w + 13]$ | $\phantom{-}e^{2} + e - 9$ |
73 | $[73, 73, w^{2} + 3w + 3]$ | $\phantom{-}2e^{3} + 3e^{2} - 15e - 15$ |
97 | $[97, 97, w^{2} + w - 15]$ | $-3e^{3} - 2e^{2} + 14e + 6$ |
101 | $[101, 101, w^{2} + 3w - 1]$ | $\phantom{-}3e^{3} + 2e^{2} - 13e - 6$ |
101 | $[101, 101, w^{2} - w - 11]$ | $\phantom{-}2e^{3} + 2e^{2} - 7e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w]$ | $1$ |