Base field 4.4.2225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41,41,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 9x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w]$ | $-\frac{1}{2}e^{2} + \frac{7}{2}$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 1]$ | $\phantom{-}e$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + 4]$ | $-2e + 2$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{3}{2}$ |
| 25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $-\frac{1}{2}e^{2} - e + \frac{3}{2}$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{3}{2}w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} + e - \frac{3}{2}$ |
| 29 | $[29, 29, -w^{2} + 5]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} + e + \frac{1}{2}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $-\frac{1}{2}e^{2} + e - \frac{5}{2}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w]$ | $\phantom{-}\frac{3}{2}e^{2} - e - \frac{9}{2}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ | $-1$ |
| 59 | $[59, 59, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}4$ |
| 59 | $[59, 59, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 1]$ | $\phantom{-}2e^{2} - 2e - 8$ |
| 61 | $[61, 61, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} + e + \frac{5}{2}$ |
| 61 | $[61, 61, -2w^{2} + w + 7]$ | $\phantom{-}e^{2} - 2e - 9$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 6]$ | $-2e - 2$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} - \frac{1}{2}w - 5]$ | $-e^{2} + 2e + 3$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}2e^{2} - 4e - 14$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}e^{2} - 9$ |
| 81 | $[81, 3, -3]$ | $-e^{2} - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ | $1$ |