Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^5 - x^4 - 5 x^3 + 2 x^2 + 3 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w - 1]$ |
| Dimension: | $2$ |
| 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:
| \(x^2 - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^4 - 6 w^2 - 2 w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^4 + w^3 + 5 w^2 - w - 4]$ | $-3$ |
| 11 | $[11, 11, -2 w^4 + w^3 + 10 w^2 + w - 3]$ | $-\frac{1}{2} e + 3$ |
| 11 | $[11, 11, w^4 - 6 w^2 - 3 w + 3]$ | $-\frac{1}{2} e + 3$ |
| 17 | $[17, 17, w^2 - 2]$ | $\phantom{-}5$ |
| 23 | $[23, 23, -w^3 + w^2 + 3 w]$ | $-\frac{3}{2} e - 3$ |
| 27 | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, 2 w^4 - 2 w^3 - 9 w^2 + 2 w + 3]$ | $-e - 1$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}\frac{5}{2} e$ |
| 47 | $[47, 47, w^4 - 2 w^3 - 3 w^2 + 5 w]$ | $-e + 4$ |
| 47 | $[47, 47, w^3 - w^2 - 4 w - 1]$ | $-4$ |
| 53 | $[53, 53, -w^4 + 7 w^2 - 3]$ | $\phantom{-}e + 7$ |
| 53 | $[53, 53, 2 w^4 - 2 w^3 - 9 w^2 + 2 w + 2]$ | $\phantom{-}2 e - 1$ |
| 53 | $[53, 53, 3 w^4 - 2 w^3 - 16 w^2 + 8]$ | $\phantom{-}e + 7$ |
| 67 | $[67, 67, -w^4 + 6 w^2 + 4 w - 3]$ | $\phantom{-}\frac{1}{2} e - 1$ |
| 73 | $[73, 73, 2 w^4 - 12 w^2 - 4 w + 5]$ | $\phantom{-}\frac{5}{2} e + 2$ |
| 83 | $[83, 83, w^4 - 5 w^2 - 3 w + 3]$ | $\phantom{-}\frac{1}{2} e - 11$ |
| 97 | $[97, 97, -w^4 + w^3 + 5 w^2 - 3 w - 3]$ | $\phantom{-}2 e + 4$ |
| 103 | $[103, 103, 2 w^3 - 3 w^2 - 7 w + 3]$ | $\phantom{-}\frac{3}{2} e + 1$ |
| 109 | $[109, 109, -3 w^4 + 2 w^3 + 14 w^2 + w - 6]$ | $\phantom{-}\frac{7}{2} e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w - 1]$ | $-1$ |