Base field 4.4.11348.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 5 x^2 + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, -w^3 + 2 w^2 + 3 w - 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 - 19 x^2 + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^3 - w^2 - 4 w + 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^2 + w + 3]$ | $-e^2 + 10$ |
| 19 | $[19, 19, -2 w + 1]$ | $\phantom{-}\frac{1}{3} e^3 - \frac{16}{3} e$ |
| 29 | $[29, 29, -w^3 + w^2 + 2 w - 1]$ | $-\frac{1}{3} e^3 + \frac{10}{3} e$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 3 w - 5]$ | $-\frac{1}{3} e^3 + \frac{13}{3} e$ |
| 37 | $[37, 37, -w^3 + 2 w^2 + 5 w - 5]$ | $\phantom{-}\frac{2}{3} e^3 - \frac{26}{3} e$ |
| 43 | $[43, 43, -2 w^3 + 2 w^2 + 8 w + 3]$ | $-4$ |
| 43 | $[43, 43, -w^2 + 3 w + 1]$ | $\phantom{-}\frac{1}{3} e^3 - \frac{25}{3} e$ |
| 47 | $[47, 47, -w^3 + 2 w^2 + 3 w - 1]$ | $\phantom{-}e^2 - 4$ |
| 53 | $[53, 53, -w^3 + w^2 + 6 w + 1]$ | $-\frac{1}{3} e^3 + \frac{19}{3} e$ |
| 59 | $[59, 59, 2 w^3 - 2 w^2 - 10 w + 3]$ | $\phantom{-}3 e$ |
| 61 | $[61, 61, w^3 - w^2 - 6 w + 3]$ | $\phantom{-}\frac{1}{3} e^3 - \frac{7}{3} e$ |
| 61 | $[61, 61, w^2 + w - 3]$ | $-\frac{1}{3} e^3 + \frac{22}{3} e$ |
| 71 | $[71, 71, -w^3 + 5 w + 1]$ | $-e^2 + 4$ |
| 71 | $[71, 71, w^3 - w^2 - 4 w - 3]$ | $\phantom{-}e^2 - 4$ |
| 81 | $[81, 3, -3]$ | $-e^2 + 14$ |
| 83 | $[83, 83, -3 w^3 + 5 w^2 + 12 w - 9]$ | $\phantom{-}e^2 - 4$ |
| 83 | $[83, 83, -3 w^3 + 6 w^2 + 13 w - 13]$ | $-\frac{1}{3} e^3 + \frac{19}{3} e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, w + 1]$ | $-1$ |