Base field 4.4.7053.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[39, 39, -w^{3} + 3w^{2} + 2w - 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $-2$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 5]$ | $-1$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 2]$ | $-e - 2$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} + 1$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{1}{2}e^{2} + e + 4$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - 2e - 6$ |
| 29 | $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ | $\phantom{-}2e - 2$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 2]$ | $-2e$ |
| 47 | $[47, 47, -w^{3} + 4w^{2} - w - 5]$ | $-4$ |
| 53 | $[53, 53, -w^{3} + 4w^{2} - w - 7]$ | $\phantom{-}\frac{1}{2}e^{2} - 12$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 1]$ | $\phantom{-}2e^{2} - 4e - 16$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 4w + 4]$ | $\phantom{-}\frac{5}{2}e^{2} - 2e - 14$ |
| 71 | $[71, 71, w^{3} - 3w^{2} - 2w + 2]$ | $-e^{2} + e + 4$ |
| 79 | $[79, 79, w^{2} - 3w - 4]$ | $-2e^{2} + 2e + 12$ |
| 83 | $[83, 83, 2w^{2} - 3w - 4]$ | $\phantom{-}e^{2} - 2e - 12$ |
| 89 | $[89, 89, -3w^{3} + 7w^{2} + 8w - 11]$ | $-e^{2} + 3e + 2$ |
| 101 | $[101, 101, w^{3} - 2w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e$ |
| 103 | $[103, 103, -2w^{3} + 4w^{2} + 5w - 1]$ | $-\frac{1}{2}e^{2} + 4e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $13$ | $[13, 13, w^{3} - 3w^{2} - w + 5]$ | $1$ |