Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, w^{2} + w - 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 6x^{3} - 39x^{2} - 144x - 108\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}0$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $-\frac{2}{9}e^{3} - e^{2} + \frac{32}{3}e + 16$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{2}{9}e^{3} - e^{2} + \frac{29}{3}e + 16$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $-\frac{1}{18}e^{3} - \frac{1}{6}e^{2} + \frac{8}{3}e + 2$ |
| 19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $-\frac{5}{18}e^{3} - \frac{7}{6}e^{2} + \frac{37}{3}e + 18$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}\frac{2}{9}e^{3} + e^{2} - \frac{32}{3}e - 16$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{3}e^{3} - \frac{5}{3}e^{2} + 14e + 28$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - 15e - 20$ |
| 43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $-\frac{1}{18}e^{3} - \frac{1}{6}e^{2} + \frac{8}{3}e + 2$ |
| 67 | $[67, 67, w^{2} - w - 5]$ | $-\frac{2}{3}e^{3} - 3e^{2} + 32e + 56$ |
| 67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - 15e - 20$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}2$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $\phantom{-}\frac{4}{9}e^{3} + 2e^{2} - \frac{64}{3}e - 36$ |
| 81 | $[81, 3, -3]$ | $-\frac{2}{9}e^{3} - e^{2} + \frac{32}{3}e + 26$ |
| 83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $\phantom{-}\frac{5}{18}e^{3} + \frac{3}{2}e^{2} - \frac{34}{3}e - 26$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}\frac{2}{9}e^{3} + e^{2} - \frac{32}{3}e - 16$ |
| 89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $-\frac{1}{9}e^{3} - e^{2} + \frac{10}{3}e + 20$ |
| 89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $\phantom{-}\frac{1}{9}e^{3} - \frac{19}{3}e + 4$ |
| 97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $-\frac{4}{9}e^{3} - 2e^{2} + \frac{64}{3}e + 34$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $-1$ |