Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 5 x^2 + 2 x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - 2 x^2 - x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^3 + 3 w^2 + w - 2]$ | $\phantom{-}2 e^2 - 2 e - 3$ |
| 11 | $[11, 11, -w^3 + 3 w^2 + 2 w - 5]$ | $\phantom{-}2 e^2 - 6 e - 2$ |
| 13 | $[13, 13, w^3 - 2 w^2 - 4 w + 2]$ | $\phantom{-}e^2 - e - 6$ |
| 13 | $[13, 13, -w + 2]$ | $-1$ |
| 17 | $[17, 17, w^3 - 3 w^2 - 2 w + 2]$ | $-e^2 + 4 e$ |
| 19 | $[19, 19, -w^2 + w + 4]$ | $\phantom{-}2 e^2 - e - 2$ |
| 19 | $[19, 19, w^3 - 2 w^2 - 3 w + 2]$ | $-3 e^2 + 5 e + 6$ |
| 23 | $[23, 23, w^2 - 2 w - 1]$ | $\phantom{-}2 e^2 - 2 e - 1$ |
| 27 | $[27, 3, w^3 - 2 w^2 - 5 w - 1]$ | $\phantom{-}3 e^2 - 6$ |
| 29 | $[29, 29, -w^3 + 2 w^2 + 5 w - 1]$ | $-2 e^2 + 8 e - 1$ |
| 37 | $[37, 37, -w^3 + 2 w^2 + 5 w - 4]$ | $\phantom{-}2 e^2 - 7 e$ |
| 41 | $[41, 41, 2 w^3 - 5 w^2 - 6 w + 4]$ | $-6 e + 4$ |
| 53 | $[53, 53, w^3 - 2 w^2 - 3 w - 2]$ | $\phantom{-}4 e^2 - 2 e - 11$ |
| 59 | $[59, 59, w - 4]$ | $-e^2 + e + 10$ |
| 67 | $[67, 67, 2 w^2 - 3 w - 8]$ | $-4 e^2 + 10 e + 4$ |
| 73 | $[73, 73, 2 w^3 - 5 w^2 - 6 w + 5]$ | $\phantom{-}6 e^2 - 10 e - 7$ |
| 89 | $[89, 89, -2 w^3 + 6 w^2 + 5 w - 7]$ | $\phantom{-}3 e - 8$ |
| 97 | $[97, 97, -2 w^3 + 6 w^2 + 3 w - 7]$ | $-5 e^2 + 10$ |
| 97 | $[97, 97, -w^3 + 3 w^2 + 3 w - 1]$ | $-2 e - 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w + 2]$ | $1$ |