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: | $[9, 3, w^{2} - 3w - 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 11x^{6} + 40x^{4} - 55x^{2} + 24\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{9}{2}e^{5} + 12e^{3} - \frac{19}{2}e$ |
3 | $[3, 3, w^{2} - w - 9]$ | $\phantom{-}0$ |
7 | $[7, 7, w^{2} - w - 7]$ | $-e^{6} + 8e^{4} - 18e^{2} + 11$ |
11 | $[11, 11, w^{2} - w - 1]$ | $-e^{7} + 10e^{5} - 30e^{3} + 25e$ |
13 | $[13, 13, -2w - 1]$ | $\phantom{-}2e^{4} - 13e^{2} + 14$ |
17 | $[17, 17, -2w^{2} + 6w + 5]$ | $-e^{5} + 8e^{3} - 12e$ |
31 | $[31, 31, -2w^{2} + 2w + 19]$ | $\phantom{-}e^{6} - 11e^{4} + 35e^{2} - 31$ |
37 | $[37, 37, 2w^{2} - 13]$ | $-e^{6} + 6e^{4} - 6e^{2} - 1$ |
41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}e^{7} - 8e^{5} + 14e^{3} + 2e$ |
43 | $[43, 43, 2w^{2} - 2w - 17]$ | $\phantom{-}e^{6} - 9e^{4} + 21e^{2} - 7$ |
43 | $[43, 43, -2w + 7]$ | $\phantom{-}2e^{6} - 17e^{4} + 39e^{2} - 25$ |
43 | $[43, 43, 12w^{2} - 8w - 101]$ | $-e^{4} + 6e^{2} - 7$ |
49 | $[49, 7, w^{2} + w - 1]$ | $\phantom{-}2e^{6} - 16e^{4} + 38e^{2} - 31$ |
59 | $[59, 59, -w^{2} + w + 11]$ | $\phantom{-}2e^{7} - 19e^{5} + 53e^{3} - 40e$ |
61 | $[61, 61, -w^{2} - w - 1]$ | $\phantom{-}2e^{6} - 19e^{4} + 53e^{2} - 43$ |
79 | $[79, 79, -2w^{2} + 4w + 7]$ | $\phantom{-}4e^{6} - 38e^{4} + 103e^{2} - 76$ |
83 | $[83, 83, 2w - 1]$ | $-2e^{7} + 18e^{5} - 46e^{3} + 25e$ |
89 | $[89, 89, 5w^{2} - 3w - 43]$ | $\phantom{-}4e^{7} - 38e^{5} + 105e^{3} - 78e$ |
103 | $[103, 103, -2w + 5]$ | $\phantom{-}2e^{6} - 19e^{4} + 49e^{2} - 31$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{2} - w - 9]$ | $1$ |