Base field 4.4.8768.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[28,14,w^{3} - 2w^{2} - 2w + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x^{2} - 10x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $-1$ |
| 7 | $[7, 7, w]$ | $-e$ |
| 7 | $[7, 7, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 4$ |
| 7 | $[7, 7, w^{2} - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{3}{2}e^{2} + \frac{15}{2}e + 7$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e^{2} - 4e - 2$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{9}{2}e - 11$ |
| 31 | $[31, 31, -w^{2} + 2w + 4]$ | $-e - 2$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ | $-\frac{3}{2}e^{2} + \frac{17}{2}e + 8$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w - 3]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{13}{2}e - 5$ |
| 47 | $[47, 47, w^{2} - 2w - 5]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{11}{2}e - 10$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}e^{2} - 3e + 2$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e + 1$ |
| 71 | $[71, 71, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}2e^{2} - 6e - 8$ |
| 79 | $[79, 79, -w - 3]$ | $-3e^{2} + 11e + 18$ |
| 79 | $[79, 79, w - 4]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 9$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 7$ |
| 89 | $[89, 89, w^{2} - 3w - 2]$ | $\phantom{-}e^{2} - 5e - 2$ |
| 89 | $[89, 89, w^{2} + w - 4]$ | $-4e^{2} + 17e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-w^{2} + w + 3]$ | $1$ |
| $7$ | $[7,7,-w + 1]$ | $1$ |