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: | $[8, 8, 4w^{2} - 3w - 34]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + x^{5} - 7x^{4} - 7x^{3} + 6x^{2} + 6x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}0$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{2} - w - 9]$ | $-2e^{5} - e^{4} + 14e^{3} + 7e^{2} - 13e - 5$ |
7 | $[7, 7, w^{2} - w - 7]$ | $\phantom{-}2e^{5} + e^{4} - 15e^{3} - 7e^{2} + 18e + 5$ |
11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}e^{3} - 5e - 2$ |
13 | $[13, 13, -2w - 1]$ | $\phantom{-}e^{5} + e^{4} - 8e^{3} - 8e^{2} + 12e + 8$ |
17 | $[17, 17, -2w^{2} + 6w + 5]$ | $\phantom{-}e^{5} - 7e^{3} + 6e + 1$ |
31 | $[31, 31, -2w^{2} + 2w + 19]$ | $-e^{5} + 8e^{3} + e^{2} - 12e - 7$ |
37 | $[37, 37, 2w^{2} - 13]$ | $\phantom{-}3e^{5} + 3e^{4} - 21e^{3} - 19e^{2} + 20e + 8$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-3e^{5} - 2e^{4} + 20e^{3} + 14e^{2} - 16e - 9$ |
43 | $[43, 43, 2w^{2} - 2w - 17]$ | $-3e^{5} - e^{4} + 21e^{3} + 9e^{2} - 21e - 13$ |
43 | $[43, 43, -2w + 7]$ | $\phantom{-}e^{5} - 6e^{3} - e^{2} - e + 1$ |
43 | $[43, 43, 12w^{2} - 8w - 101]$ | $-6e^{5} - 5e^{4} + 43e^{3} + 32e^{2} - 42e - 18$ |
49 | $[49, 7, w^{2} + w - 1]$ | $-4e^{5} + 30e^{3} + e^{2} - 37e - 3$ |
59 | $[59, 59, -w^{2} + w + 11]$ | $\phantom{-}9e^{5} + 6e^{4} - 64e^{3} - 40e^{2} + 61e + 28$ |
61 | $[61, 61, -w^{2} - w - 1]$ | $\phantom{-}3e^{5} - 20e^{3} + e^{2} + 12e - 4$ |
79 | $[79, 79, -2w^{2} + 4w + 7]$ | $-5e^{5} - 6e^{4} + 36e^{3} + 38e^{2} - 36e - 22$ |
83 | $[83, 83, 2w - 1]$ | $\phantom{-}5e^{5} + 6e^{4} - 36e^{3} - 41e^{2} + 33e + 22$ |
89 | $[89, 89, 5w^{2} - 3w - 43]$ | $\phantom{-}2e^{4} - e^{3} - 17e^{2} + 6e + 14$ |
103 | $[103, 103, -2w + 5]$ | $-14e^{5} - 8e^{4} + 101e^{3} + 53e^{2} - 101e - 39$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{2} + 2w + 2]$ | $1$ |