Base field 4.4.5125.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 34x^{4} + 296x^{2} - 148\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{2} + 2w + 3]$ | $-\frac{5}{29}e^{4} + \frac{84}{29}e^{2} - \frac{12}{29}$ |
9 | $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ | $\phantom{-}e$ |
9 | $[9, 3, -w^{3} + 5w + 5]$ | $\phantom{-}e$ |
11 | $[11, 11, w]$ | $-\frac{1}{29}e^{4} + \frac{11}{29}e^{2} + \frac{102}{29}$ |
11 | $[11, 11, w - 1]$ | $-\frac{1}{29}e^{4} + \frac{11}{29}e^{2} + \frac{102}{29}$ |
16 | $[16, 2, 2]$ | $-1$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{58}e^{5} + \frac{9}{29}e^{3} - \frac{283}{29}e$ |
19 | $[19, 19, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{58}e^{5} + \frac{9}{29}e^{3} - \frac{283}{29}e$ |
29 | $[29, 29, w^{3} - 4w^{2} - w + 10]$ | $\phantom{-}\frac{7}{58}e^{5} - \frac{82}{29}e^{3} + \frac{368}{29}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + w - 7]$ | $\phantom{-}\frac{7}{58}e^{5} - \frac{82}{29}e^{3} + \frac{368}{29}e$ |
41 | $[41, 41, 3w^{2} - 2w - 10]$ | $\phantom{-}\frac{14}{29}e^{4} - \frac{270}{29}e^{2} + \frac{486}{29}$ |
49 | $[49, 7, -2w^{2} + 3w + 8]$ | $-\frac{2}{29}e^{5} + \frac{51}{29}e^{3} - \frac{289}{29}e$ |
49 | $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ | $-\frac{2}{29}e^{5} + \frac{51}{29}e^{3} - \frac{289}{29}e$ |
71 | $[71, 71, -w - 3]$ | $-\frac{4}{29}e^{4} + \frac{44}{29}e^{2} + \frac{118}{29}$ |
71 | $[71, 71, w - 4]$ | $-\frac{4}{29}e^{4} + \frac{44}{29}e^{2} + \frac{118}{29}$ |
79 | $[79, 79, -w^{3} + w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{29}e^{5} - \frac{40}{29}e^{3} + \frac{420}{29}e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}\frac{1}{29}e^{5} - \frac{40}{29}e^{3} + \frac{420}{29}e$ |
89 | $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ | $-\frac{1}{29}e^{5} + \frac{11}{29}e^{3} + \frac{15}{29}e$ |
89 | $[89, 89, w^{3} - 6w - 2]$ | $-\frac{1}{29}e^{5} + \frac{11}{29}e^{3} + \frac{15}{29}e$ |
101 | $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ | $-\frac{1}{29}e^{4} + \frac{40}{29}e^{2} - \frac{188}{29}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$16$ | $[16, 2, 2]$ | $1$ |