Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^4 - 6 x^2 + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^3 - 4 w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 - 7 x^4 + 13 x^2 - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^2 + w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^2 - w - 3]$ | $-e^3 + 3 e$ |
| 11 | $[11, 11, -w^2 + w + 1]$ | $\phantom{-}e^5 - 5 e^3 + 4 e$ |
| 11 | $[11, 11, -w^2 - w + 1]$ | $-e^5 + 6 e^3 - 8 e$ |
| 13 | $[13, 13, w^3 - 4 w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^3 + 4 w + 1]$ | $-e^4 + 3 e^2 - 1$ |
| 25 | $[25, 5, -w^2 - 2 w + 1]$ | $\phantom{-}e^4 - 8 e^2 + 9$ |
| 25 | $[25, 5, w^2 - 2 w - 1]$ | $\phantom{-}4 e^2 - 11$ |
| 37 | $[37, 37, w^3 - 3 w - 1]$ | $-2 e^4 + 9 e^2 - 7$ |
| 37 | $[37, 37, w^3 - 3 w + 1]$ | $-2 e^4 + 9 e^2 - 7$ |
| 59 | $[59, 59, w^2 - w - 5]$ | $-2 e^5 + 8 e^3 - 2 e$ |
| 59 | $[59, 59, -w^2 - w + 5]$ | $\phantom{-}3 e^5 - 12 e^3 + 4 e$ |
| 61 | $[61, 61, -w^3 + w^2 + 4 w - 7]$ | $\phantom{-}e^4 - 2 e^2 + 3$ |
| 61 | $[61, 61, w^3 - 3 w^2 - 6 w + 11]$ | $\phantom{-}6 e^4 - 28 e^2 + 18$ |
| 73 | $[73, 73, 2 w^2 - w - 5]$ | $\phantom{-}5 e^4 - 23 e^2 + 16$ |
| 73 | $[73, 73, 2 w - 1]$ | $\phantom{-}3 e^4 - 15 e^2 + 9$ |
| 73 | $[73, 73, -2 w - 1]$ | $-6 e^4 + 27 e^2 - 21$ |
| 73 | $[73, 73, 2 w^2 + w - 5]$ | $\phantom{-}2 e^4 - 8 e^2 - 4$ |
| 83 | $[83, 83, 2 w^3 + w^2 - 9 w - 7]$ | $-4 e^5 + 26 e^3 - 34 e$ |
| 83 | $[83, 83, -2 w^3 + w^2 + 7 w + 1]$ | $\phantom{-}2 e^5 - 9 e^3 + 5 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,w^3-4 w+1]$ | $-1$ |