Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 10x^{3} + 18x^{2} - 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}e$ |
9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $-e^{4} + 10e^{2} - 7e - 4$ |
11 | $[11, 11, w - 1]$ | $-2e^{4} + 19e^{2} - 18e - 2$ |
25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}e^{4} - 10e^{2} + 10e + 4$ |
29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 7e + 8$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |
49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $-2e^{4} + 2e^{3} + 22e^{2} - 32e$ |
59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $-e^{4} + 10e^{2} - 10e - 2$ |
59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-3e^{4} + 29e^{2} - 24e - 6$ |
61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $-2e^{2} - 2e + 12$ |
61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $\phantom{-}e^{4} - 10e^{2} + 8e - 4$ |
64 | $[64, 2, 2]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 3$ |
71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $-4e^{3} - 4e^{2} + 30e - 8$ |
71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $\phantom{-}e^{2} + 2e + 4$ |
79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $-e^{4} - 2e^{3} + 9e^{2} + 8e - 4$ |
81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $-5e^{4} + 47e^{2} - 46e - 2$ |
89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $-2e^{4} + 18e^{2} - 19e + 4$ |
89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $\phantom{-}4e^{4} + e^{3} - 38e^{2} + 26e + 12$ |
89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $-5e^{4} + 48e^{2} - 46e - 6$ |
89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $-3e^{4} + 30e^{2} - 26e - 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $1$ |