Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 4, w^{2} - 3w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{3} - 6x^{2} - 21x - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}0$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
3 | $[3, 3, w^{2} - w - 9]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{2} - w - 7]$ | $-e^{3} - 2e^{2} + 8e + 11$ |
11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}e^{3} + e^{2} - 9e - 9$ |
13 | $[13, 13, -2w - 1]$ | $\phantom{-}e^{2} - e - 7$ |
17 | $[17, 17, -2w^{2} + 6w + 5]$ | $-e^{3} - e^{2} + 6e + 3$ |
31 | $[31, 31, -2w^{2} + 2w + 19]$ | $\phantom{-}2e + 2$ |
37 | $[37, 37, 2w^{2} - 13]$ | $-2e^{3} - 4e^{2} + 14e + 20$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-e^{3} - 2e^{2} + 9e + 6$ |
43 | $[43, 43, 2w^{2} - 2w - 17]$ | $\phantom{-}3e^{3} + 4e^{2} - 25e - 28$ |
43 | $[43, 43, -2w + 7]$ | $\phantom{-}e^{3} + e^{2} - 10e - 7$ |
43 | $[43, 43, 12w^{2} - 8w - 101]$ | $\phantom{-}3e^{3} + 5e^{2} - 22e - 31$ |
49 | $[49, 7, w^{2} + w - 1]$ | $-e^{3} - 3e^{2} + 8e + 11$ |
59 | $[59, 59, -w^{2} + w + 11]$ | $\phantom{-}3e^{3} + 5e^{2} - 24e - 33$ |
61 | $[61, 61, -w^{2} - w - 1]$ | $\phantom{-}3e^{2} - 16$ |
79 | $[79, 79, -2w^{2} + 4w + 7]$ | $\phantom{-}e^{3} + 3e^{2} - 10e - 25$ |
83 | $[83, 83, 2w - 1]$ | $\phantom{-}2e^{3} + 3e^{2} - 12e - 18$ |
89 | $[89, 89, 5w^{2} - 3w - 43]$ | $\phantom{-}4e^{3} + 8e^{2} - 30e - 42$ |
103 | $[103, 103, -2w + 5]$ | $-3e^{3} - 3e^{2} + 24e + 17$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{2} + 2w + 2]$ | $-1$ |
$2$ | $[2, 2, w + 1]$ | $-1$ |