Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^4 - 6 x^2 - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, w^2 + w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 + 2 x^5 - 12 x^4 - 8 x^3 + 47 x^2 - 33 x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^3 + 5 w + 2]$ | $-1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^3 + 5 w]$ | $-e^5 - 3 e^4 + 8 e^3 + 16 e^2 - 23 e$ |
| 13 | $[13, 13, -w^3 + w^2 + 6 w - 3]$ | $\phantom{-}2 e^3 + e^2 - 16 e + 8$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^5 + 3 e^4 - 9 e^3 - 16 e^2 + 32 e - 10$ |
| 19 | $[19, 19, 2 w^3 - w^2 - 11 w + 2]$ | $\phantom{-}e^5 + 3 e^4 - 9 e^3 - 16 e^2 + 32 e - 8$ |
| 25 | $[25, 5, -w^2 + w + 3]$ | $\phantom{-}e^5 + 3 e^4 - 12 e^3 - 19 e^2 + 51 e - 17$ |
| 27 | $[27, 3, w^3 - w^2 - 5 w + 4]$ | $-2 e^5 - 6 e^4 + 16 e^3 + 29 e^2 - 53 e + 16$ |
| 31 | $[31, 31, -w - 3]$ | $-e^4 - 2 e^3 + 8 e^2 + 9 e - 10$ |
| 37 | $[37, 37, -w^3 - w^2 + 6 w + 4]$ | $-e^4 - e^3 + 7 e^2 - 2 e - 5$ |
| 41 | $[41, 41, w^3 + w^2 - 6 w - 5]$ | $\phantom{-}e^5 + 3 e^4 - 6 e^3 - 14 e^2 + 11 e + 7$ |
| 43 | $[43, 43, w^3 - 7 w - 2]$ | $\phantom{-}e^4 - 3 e^3 - 12 e^2 + 26 e - 4$ |
| 47 | $[47, 47, -2 w^3 + 11 w + 2]$ | $-e^5 - e^4 + 15 e^3 + 5 e^2 - 56 e + 22$ |
| 61 | $[61, 61, w^2 - 3]$ | $\phantom{-}e^5 + 5 e^4 - 9 e^3 - 32 e^2 + 47 e - 12$ |
| 67 | $[67, 67, w^2 + w - 4]$ | $-e^5 - 4 e^4 + 10 e^3 + 24 e^2 - 49 e + 11$ |
| 79 | $[79, 79, -4 w^3 + 2 w^2 + 22 w - 9]$ | $-e^5 - 3 e^4 + 11 e^3 + 17 e^2 - 45 e + 20$ |
| 97 | $[97, 97, -3 w^3 + 2 w^2 + 19 w - 6]$ | $-2 e^4 - 4 e^3 + 10 e^2 + 8 e + 5$ |
| 97 | $[97, 97, -w^3 + 6 w - 3]$ | $\phantom{-}2 e^5 + 5 e^4 - 12 e^3 - 16 e^2 + 19 e - 12$ |
| 97 | $[97, 97, -3 w^3 + 16 w]$ | $\phantom{-}e^5 + 3 e^4 - 7 e^3 - 10 e^2 + 24 e - 21$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^3 + 5 w + 2]$ | $1$ |
| $5$ | $[5, 5, w - 1]$ | $-1$ |