Base field 4.4.18625.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 9x + 41\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16,4,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{2}{3}]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 17x^{2} + 71\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ | $\phantom{-}e$ |
4 | $[4, 2, w - 3]$ | $\phantom{-}0$ |
5 | $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ | $-e$ |
9 | $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ | $\phantom{-}0$ |
9 | $[9, 3, -w - 2]$ | $-e^{3} + 9e$ |
11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ | $-2e^{2} + 14$ |
11 | $[11, 11, -w + 2]$ | $\phantom{-}2e^{2} - 17$ |
41 | $[41, 41, -w]$ | $\phantom{-}4e^{2} - 32$ |
41 | $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ | $-5$ |
59 | $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ | $\phantom{-}3e^{3} - 26e$ |
59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ | $-2e$ |
61 | $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ | $-2e^{2} + 17$ |
61 | $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ | $-6e^{2} + 55$ |
61 | $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ | $-e^{2}$ |
61 | $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ | $\phantom{-}5e^{2} - 49$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ | $\phantom{-}7e^{2} - 63$ |
71 | $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ | $-7e^{2} + 56$ |
79 | $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ | $-e^{3} + 10e$ |
79 | $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ | $\phantom{-}3e^{3} - 24e$ |
89 | $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ | $\phantom{-}e^{3} - 12e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,w - 3]$ | $-1$ |