Base field 4.4.18625.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 14 x^2 + 9 x + 41\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, -\frac{1}{6} w^3 + \frac{1}{3} w + \frac{5}{6}]$ |
| 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:
| \(x^4 + 4 x^3 - 39 x^2 - 176 x - 139\) |
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 | $[11, 11, -\frac{1}{6} w^3 + \frac{7}{3} w + \frac{11}{6}]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{8}{61} e^3 - \frac{13}{61} e^2 + \frac{320}{61} e + \frac{709}{61}$ |
| 41 | $[41, 41, -w]$ | $-\frac{3}{61} e^3 + \frac{18}{61} e^2 + \frac{59}{61} e - \frac{428}{61}$ |
| 41 | $[41, 41, \frac{1}{6} w^3 - \frac{7}{3} w + \frac{1}{6}]$ | $\phantom{-}\frac{17}{61} e^3 + \frac{20}{61} e^2 - \frac{741}{61} e - \frac{1560}{61}$ |
| 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 | $[61, 61, -\frac{5}{3} w^3 - 3 w^2 + \frac{46}{3} w + \frac{79}{3}]$ | $\phantom{-}\frac{6}{61} e^3 + \frac{25}{61} e^2 - \frac{362}{61} e - \frac{852}{61}$ |
| 61 | $[61, 61, \frac{5}{6} w^3 + w^2 - \frac{23}{3} w - \frac{55}{6}]$ | $-\frac{6}{61} e^3 - \frac{25}{61} e^2 + \frac{118}{61} e + \frac{1096}{61}$ |
| 61 | $[61, 61, w^3 + 2 w^2 - 9 w - 17]$ | $\phantom{-}\frac{18}{61} e^3 + \frac{14}{61} e^2 - \frac{781}{61} e - \frac{1458}{61}$ |
| 61 | $[61, 61, -\frac{1}{6} w^3 + \frac{10}{3} w + \frac{35}{6}]$ | $\phantom{-}\frac{18}{61} e^3 + \frac{14}{61} e^2 - \frac{659}{61} e - \frac{726}{61}$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + 2 w^2 + 4 w - \frac{33}{2}]$ | $-\frac{4}{61} e^3 - \frac{37}{61} e^2 + \frac{282}{61} e + \frac{1239}{61}$ |
| 71 | $[71, 71, \frac{1}{6} w^3 - w^2 - \frac{4}{3} w + \frac{67}{6}]$ | $-\frac{18}{61} e^3 - \frac{14}{61} e^2 + \frac{659}{61} e + \frac{1214}{61}$ |
| 79 | $[79, 79, \frac{1}{2} w^3 - 3 w + \frac{1}{2}]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -\frac{2}{3} w^3 + \frac{19}{3} w - \frac{2}{3}]$ | $\phantom{-}0$ |
| 89 | $[89, 89, \frac{1}{2} w^3 + w^2 - 5 w - \frac{15}{2}]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{6} w^3 - \frac{7}{3} w - \frac{17}{6}]$ | $-1$ |