Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^5 + 4 x^4 - x^3 - 16 x^2 - 14 x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}9 e^4 + 23 e^3 - 42 e^2 - 84 e - 8$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}4 e^4 + 9 e^3 - 22 e^2 - 33 e + 5$ |
| 19 | $[19, 19, -w^2 + 6]$ | $\phantom{-}6 e^4 + 17 e^3 - 25 e^2 - 64 e - 12$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $\phantom{-}e^4 + 2 e^3 - 6 e^2 - 7 e + 4$ |
| 19 | $[19, 19, -w + 2]$ | $-5 e^4 - 12 e^3 + 25 e^2 + 43 e - 4$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $\phantom{-}2 e^4 + 5 e^3 - 10 e^2 - 17 e + 1$ |
| 29 | $[29, 29, -w^2 + 9]$ | $-e^4 - 3 e^3 + 2 e^2 + 8 e + 8$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $\phantom{-}10 e^4 + 26 e^3 - 45 e^2 - 93 e - 13$ |
| 29 | $[29, 29, w^2 - 7]$ | $-3 e^4 - 7 e^3 + 15 e^2 + 23 e - 5$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $-8 e^4 - 21 e^3 + 37 e^2 + 78 e + 3$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $-11 e^4 - 28 e^3 + 53 e^2 + 102 e - 1$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $-4 e^4 - 9 e^3 + 22 e^2 + 29 e - 7$ |
| 41 | $[41, 41, -w]$ | $-8 e^4 - 22 e^3 + 34 e^2 + 84 e + 17$ |
| 41 | $[41, 41, -w + 1]$ | $-5 e^4 - 13 e^3 + 24 e^2 + 46 e - 4$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $\phantom{-}8 e^4 + 21 e^3 - 37 e^2 - 74 e - 3$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $-7 e^4 - 21 e^3 + 28 e^2 + 82 e + 19$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $-6 e^4 - 16 e^3 + 25 e^2 + 57 e + 5$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $\phantom{-}e^3 + 4 e^2 - 2 e - 13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $-1$ |