Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^5 - x^4 - 5 x^3 + 2 x^2 + 5 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, 2 w^4 - 3 w^3 - 8 w^2 + 7 w + 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - 6 x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^4 + w^3 + 4 w^2 - 2 w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^2 - w - 2]$ | $-e$ |
| 19 | $[19, 19, w^4 - 2 w^3 - 4 w^2 + 5 w + 4]$ | $-e^2 - 1$ |
| 23 | $[23, 23, -w^3 + w^2 + 3 w - 1]$ | $-2 e^2 + 8$ |
| 29 | $[29, 29, 2 w^4 - 3 w^3 - 8 w^2 + 7 w + 4]$ | $-1$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}2 e^2 - 9$ |
| 37 | $[37, 37, w^3 - 2 w^2 - 2 w + 2]$ | $-2 e^2 - e + 7$ |
| 41 | $[41, 41, -2 w^4 + 3 w^3 + 9 w^2 - 8 w - 6]$ | $-e + 1$ |
| 43 | $[43, 43, -2 w^4 + 3 w^3 + 8 w^2 - 8 w - 6]$ | $\phantom{-}2 e - 6$ |
| 47 | $[47, 47, w^4 - 2 w^3 - 5 w^2 + 6 w + 5]$ | $-e^2 - e + 1$ |
| 53 | $[53, 53, -w^4 + w^3 + 4 w^2 - w - 4]$ | $\phantom{-}0$ |
| 61 | $[61, 61, w^2 - 2 w - 3]$ | $\phantom{-}3 e^2 - 4 e - 13$ |
| 67 | $[67, 67, w^4 - w^3 - 4 w^2 + 3 w]$ | $\phantom{-}2 e^2 + 2 e - 12$ |
| 67 | $[67, 67, -w^4 + w^3 + 5 w^2 - 2 w - 2]$ | $\phantom{-}e^2 - 2 e - 12$ |
| 71 | $[71, 71, w^4 - w^3 - 4 w^2 + 5]$ | $\phantom{-}3 e - 3$ |
| 71 | $[71, 71, w^4 - 2 w^3 - 3 w^2 + 5 w + 3]$ | $\phantom{-}e^2 + 3 e - 11$ |
| 71 | $[71, 71, 2 w^4 - 2 w^3 - 8 w^2 + 5 w + 4]$ | $\phantom{-}e^2 + 2 e - 13$ |
| 73 | $[73, 73, -2 w^4 + 2 w^3 + 9 w^2 - 5 w - 6]$ | $-4$ |
| 81 | $[81, 3, -2 w^4 + 3 w^3 + 10 w^2 - 9 w - 10]$ | $\phantom{-}3 e^2 - e - 15$ |
| 97 | $[97, 97, -2 w^4 + 3 w^3 + 7 w^2 - 5 w - 4]$ | $-2 e^2 + 3 e + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2 w^4 - 3 w^3 - 8 w^2 + 7 w + 4]$ | $1$ |