Base field 3.3.361.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[31,31,-w^{2} - w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 16x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{2}e - 1$ |
| 7 | $[7, 7, w^{2} - 4]$ | $\phantom{-}2$ |
| 7 | $[7, 7, w^{2} + w - 5]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-e + 2$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{1}{4}e^{2} + \frac{1}{2}e + 3$ |
| 11 | $[11, 11, -w^{2} - w + 6]$ | $\phantom{-}e - 2$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}\frac{1}{4}e^{2} - 4$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-\frac{3}{2}e + 2$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{2} + 6$ |
| 31 | $[31, 31, w^{2} - 8]$ | $-\frac{3}{4}e^{2} + \frac{1}{2}e + 7$ |
| 31 | $[31, 31, 2w^{2} - 9]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 2w^{2} + 2w - 9]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 4$ |
| 37 | $[37, 37, 2w^{2} + w - 8]$ | $-\frac{1}{4}e^{2} + e + 4$ |
| 37 | $[37, 37, w^{2} + 2w - 6]$ | $-\frac{1}{4}e^{2} - e + 2$ |
| 37 | $[37, 37, w^{2} - w - 5]$ | $-\frac{1}{2}e^{2} + e + 8$ |
| 83 | $[83, 83, -2w - 3]$ | $-\frac{3}{4}e^{2} + \frac{5}{2}e + 7$ |
| 83 | $[83, 83, 2w^{2} - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 6$ |
| 83 | $[83, 83, 2w^{2} + 2w - 13]$ | $-\frac{3}{4}e^{2} + e + 10$ |
| 103 | $[103, 103, 3w^{2} + 2w - 17]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 12$ |
| 103 | $[103, 103, 2w^{2} - w - 5]$ | $\phantom{-}\frac{1}{4}e^{2} - 3e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,-w^{2} - w + 1]$ | $-1$ |