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: | yes |
| 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:
| \(x^{4} + 4x^{3} - 39x^{2} - 176x - 139\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w - 3]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ | $\phantom{-}0$ |
| 9 | $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -w - 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ | $-\frac{8}{61}e^{3} - \frac{13}{61}e^{2} + \frac{320}{61}e + \frac{709}{61}$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}e$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}\frac{17}{61}e^{3} + \frac{20}{61}e^{2} - \frac{741}{61}e - \frac{1560}{61}$ |
| 41 | $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ | $-\frac{3}{61}e^{3} + \frac{18}{61}e^{2} + \frac{59}{61}e - \frac{428}{61}$ |
| 59 | $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ | $\phantom{-}0$ |
| 61 | $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ | $-\frac{6}{61}e^{3} - \frac{25}{61}e^{2} + \frac{118}{61}e + \frac{1096}{61}$ |
| 61 | $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ | $\phantom{-}\frac{6}{61}e^{3} + \frac{25}{61}e^{2} - \frac{362}{61}e - \frac{852}{61}$ |
| 61 | $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ | $\phantom{-}\frac{18}{61}e^{3} + \frac{14}{61}e^{2} - \frac{659}{61}e - \frac{726}{61}$ |
| 61 | $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ | $\phantom{-}\frac{18}{61}e^{3} + \frac{14}{61}e^{2} - \frac{781}{61}e - \frac{1458}{61}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ | $-\frac{18}{61}e^{3} - \frac{14}{61}e^{2} + \frac{659}{61}e + \frac{1214}{61}$ |
| 71 | $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ | $-\frac{4}{61}e^{3} - \frac{37}{61}e^{2} + \frac{282}{61}e + \frac{1239}{61}$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ | $\phantom{-}0$ |
| 89 | $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,w - 3]$ | $-1$ |