Base field \(\Q(\zeta_{16})^+\)
Generator \(w\), with minimal polynomial \(x^4 - 4 x^2 + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[79,79,-w^3 + w^2 + 2 w - 5]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^2 - w + 3]$ | $-2$ |
| 17 | $[17, 17, -w^3 - w^2 + 3 w + 1]$ | $-6$ |
| 17 | $[17, 17, w^3 - w^2 - 3 w + 1]$ | $\phantom{-}2$ |
| 17 | $[17, 17, w^2 - w - 3]$ | $-2$ |
| 31 | $[31, 31, w^3 + w^2 - 2 w - 3]$ | $-8$ |
| 31 | $[31, 31, -w^3 + w^2 + 4 w - 1]$ | $\phantom{-}4$ |
| 31 | $[31, 31, w^3 + w^2 - 4 w - 1]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -w^3 + w^2 + 2 w - 3]$ | $-8$ |
| 47 | $[47, 47, -2 w^3 + w^2 + 5 w - 1]$ | $\phantom{-}8$ |
| 47 | $[47, 47, 2 w^3 + w^2 - 6 w - 1]$ | $-8$ |
| 47 | $[47, 47, -2 w^3 + w^2 + 6 w - 1]$ | $-8$ |
| 47 | $[47, 47, 2 w^3 + w^2 - 5 w - 1]$ | $-12$ |
| 49 | $[49, 7, w^2 + 1]$ | $-6$ |
| 49 | $[49, 7, -2 w^2 + 3]$ | $-2$ |
| 79 | $[79, 79, -w^3 - w^2 + 4 w - 1]$ | $-8$ |
| 79 | $[79, 79, -w^3 + w^2 + 2 w - 5]$ | $\phantom{-}1$ |
| 79 | $[79, 79, w^3 + w^2 - 2 w - 5]$ | $\phantom{-}12$ |
| 79 | $[79, 79, w^3 - w^2 - 4 w - 1]$ | $-4$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79,79,-w^3 + w^2 + 2 w - 5]$ | $-1$ |