Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 9 x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 4, -w]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - x^2 - 9 x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 2]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^2 + 3 w + 3]$ | $-e^2 - e + 7$ |
| 9 | $[9, 3, -w^2 + 2 w + 7]$ | $-e^2 - e + 7$ |
| 13 | $[13, 13, w + 3]$ | $-3$ |
| 13 | $[13, 13, -w + 3]$ | $\phantom{-}e^2 - 7$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}e^2 - 3$ |
| 17 | $[17, 17, -w^2 - 2 w + 1]$ | $-2 e^2 - 2 e + 15$ |
| 23 | $[23, 23, w^2 - 2 w - 5]$ | $\phantom{-}e^2 + 2 e - 8$ |
| 31 | $[31, 31, 2 w + 3]$ | $-e^2 + e + 6$ |
| 31 | $[31, 31, -2 w^2 + 3 w + 15]$ | $\phantom{-}e - 2$ |
| 31 | $[31, 31, 3 w + 7]$ | $-e^2 - 2 e + 14$ |
| 37 | $[37, 37, 3 w^2 - 4 w - 27]$ | $\phantom{-}2 e^2 - 10$ |
| 41 | $[41, 41, -2 w^2 + 7 w + 1]$ | $-1$ |
| 59 | $[59, 59, w^2 - 3]$ | $\phantom{-}3 e^2 + 4 e - 26$ |
| 61 | $[61, 61, 4 w^2 - 12 w - 11]$ | $\phantom{-}2 e^2 + 2 e - 7$ |
| 71 | $[71, 71, w^2 - 2 w - 11]$ | $-2 e^2 - 3 e + 24$ |
| 97 | $[97, 97, 3 w + 5]$ | $\phantom{-}11$ |
| 101 | $[101, 101, 2 w^2 - 6 w - 7]$ | $\phantom{-}e^2 + 5$ |
| 103 | $[103, 103, 2 w^2 - 3 w - 19]$ | $\phantom{-}3 e^2 + e - 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 2]$ | $-1$ |