Base field 3.3.321.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[43, 43, w^{2} - 3w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} - 4x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{3}{2}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 4$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{7}{2}$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-e^{3} + 2e^{2} + 4e - 6$ |
| 23 | $[23, 23, -w - 3]$ | $\phantom{-}e^{3} - e^{2} - 6e + 2$ |
| 29 | $[29, 29, -w^{2} + 2w + 4]$ | $-\frac{3}{2}e^{3} + \frac{5}{2}e^{2} + \frac{17}{2}e - \frac{17}{2}$ |
| 31 | $[31, 31, 2w - 3]$ | $-3e + 1$ |
| 41 | $[41, 41, -2w^{2} + 3w + 6]$ | $-e^{3} + 2e^{2} + 4e - 7$ |
| 43 | $[43, 43, w^{2} - 3w + 3]$ | $-1$ |
| 47 | $[47, 47, w^{2} + w - 4]$ | $\phantom{-}2e^{2} - 3e - 7$ |
| 49 | $[49, 7, 2w^{2} - 3w - 3]$ | $\phantom{-}2e^{3} - 3e^{2} - 10e + 10$ |
| 53 | $[53, 53, w^{2} - 3w - 2]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{7}{2}e^{2} - \frac{31}{2}e + \frac{7}{2}$ |
| 59 | $[59, 59, 2w^{2} - w - 5]$ | $\phantom{-}4e^{3} - 6e^{2} - 21e + 9$ |
| 59 | $[59, 59, w^{2} - w - 7]$ | $-\frac{3}{2}e^{3} + \frac{3}{2}e^{2} + \frac{19}{2}e - \frac{1}{2}$ |
| 59 | $[59, 59, -w^{2} - w + 7]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{9}{2}e + \frac{23}{2}$ |
| 67 | $[67, 67, 2w^{2} - 3w - 7]$ | $-2e^{2} + 2e + 8$ |
| 73 | $[73, 73, -w^{2} + 4w - 5]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{3}{2}e^{2} - \frac{27}{2}e - \frac{9}{2}$ |
| 79 | $[79, 79, w^{2} - 8]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
| 79 | $[79, 79, w^{2} - 5w + 5]$ | $-e^{3} + e^{2} + 4e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43, 43, w^{2} - 3w + 3]$ | $1$ |