Base field 6.6.434581.1
Generator \(w\), with minimal polynomial \(x^6 - 2 x^5 - 4 x^4 + 5 x^3 + 4 x^2 - 2 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[13,13,w^2 - w - 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 + 2 x - 53\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, -w^5 + 3 w^4 + 2 w^3 - 9 w^2 + w + 4]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^2 + w + 2]$ | $-1$ |
| 27 | $[27, 3, 2 w^5 - 4 w^4 - 7 w^3 + 9 w^2 + 4 w - 2]$ | $\phantom{-}2$ |
| 27 | $[27, 3, -2 w^5 + 5 w^4 + 5 w^3 - 12 w^2 - w + 5]$ | $\phantom{-}e$ |
| 29 | $[29, 29, w^3 - 2 w^2 - 2 w + 3]$ | $\phantom{-}6$ |
| 29 | $[29, 29, 2 w^5 - 4 w^4 - 7 w^3 + 8 w^2 + 4 w - 2]$ | $\phantom{-}e + 4$ |
| 43 | $[43, 43, -w^5 + 3 w^4 + w^3 - 6 w^2 + 3 w + 1]$ | $\phantom{-}7$ |
| 43 | $[43, 43, -w^4 + w^3 + 5 w^2 - 4]$ | $-e - 6$ |
| 49 | $[49, 7, w^5 - 4 w^4 + 11 w^2 - 3 w - 4]$ | $-4$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}e - 4$ |
| 71 | $[71, 71, 2 w^5 - 6 w^4 - 4 w^3 + 17 w^2 - w - 6]$ | $-2 e - 2$ |
| 71 | $[71, 71, 2 w^4 - 4 w^3 - 6 w^2 + 7 w + 2]$ | $-6$ |
| 71 | $[71, 71, -w^5 + 3 w^4 + 2 w^3 - 7 w^2 - w]$ | $\phantom{-}9$ |
| 71 | $[71, 71, -2 w^5 + 5 w^4 + 6 w^3 - 14 w^2 - 3 w + 5]$ | $-e - 4$ |
| 83 | $[83, 83, -3 w^5 + 7 w^4 + 9 w^3 - 17 w^2 - 5 w + 5]$ | $\phantom{-}6$ |
| 83 | $[83, 83, 3 w^5 - 6 w^4 - 10 w^3 + 12 w^2 + 5 w - 2]$ | $-2 e - 5$ |
| 83 | $[83, 83, -2 w^5 + 5 w^4 + 5 w^3 - 11 w^2 - 3 w + 3]$ | $\phantom{-}6$ |
| 83 | $[83, 83, 3 w^5 - 7 w^4 - 8 w^3 + 15 w^2 + 2 w - 4]$ | $\phantom{-}2 e + 2$ |
| 97 | $[97, 97, -3 w^5 + 6 w^4 + 10 w^3 - 12 w^2 - 5 w + 3]$ | $-e - 6$ |
| 97 | $[97, 97, w^5 - 2 w^4 - 4 w^3 + 5 w^2 + 5 w - 3]$ | $-2 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,w^2 - w - 2]$ | $1$ |