Base field 4.4.13888.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 34x^{2} + 200\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ | $-1$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{7}{10}e$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{7}{10}e$ |
| 9 | $[9, 3, w]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ | $-\frac{1}{2}e^{2} + 11$ |
| 23 | $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ | $-\frac{1}{2}e^{2} + 11$ |
| 31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ | $-e^{2} + 16$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ | $-\frac{1}{5}e^{3} + \frac{29}{5}e$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ | $-\frac{1}{5}e^{3} + \frac{29}{5}e$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{12}{5}e$ |
| 47 | $[47, 47, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{12}{5}e$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ | $-\frac{1}{5}e^{3} + \frac{24}{5}e$ |
| 73 | $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ | $-e^{2} + 18$ |
| 73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-e^{2} + 18$ |
| 73 | $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ | $-\frac{1}{5}e^{3} + \frac{24}{5}e$ |
| 79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{43}{5}e$ |
| 79 | $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{43}{5}e$ |
| 97 | $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ | $-\frac{3}{20}e^{3} + \frac{11}{10}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ | $1$ |