Base field \(\Q(\sqrt{5}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight | [2, 2] |
Level | $[116,58,-2w + 12]$ |
Label | 2.2.5.1-116.2-a |
Dimension | 1 |
Is CM | no |
Is base change | no |
Parent newspace dimension | 2 |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, -2w + 1]$ | $\phantom{-}1$ |
9 | $[9, 3, 3]$ | $\phantom{-}0$ |
11 | $[11, 11, -3w + 2]$ | $-3$ |
11 | $[11, 11, -3w + 1]$ | $\phantom{-}2$ |
19 | $[19, 19, -4w + 3]$ | $\phantom{-}0$ |
19 | $[19, 19, -4w + 1]$ | $-5$ |
29 | $[29, 29, w + 5]$ | $-5$ |
29 | $[29, 29, -w + 6]$ | $-1$ |
31 | $[31, 31, -5w + 2]$ | $-8$ |
31 | $[31, 31, -5w + 3]$ | $\phantom{-}7$ |
41 | $[41, 41, -6w + 5]$ | $\phantom{-}12$ |
41 | $[41, 41, w - 7]$ | $-3$ |
49 | $[49, 7, -7]$ | $\phantom{-}5$ |
59 | $[59, 59, 2w - 9]$ | $\phantom{-}0$ |
59 | $[59, 59, 7w - 5]$ | $\phantom{-}0$ |
61 | $[61, 61, 3w - 10]$ | $\phantom{-}2$ |
61 | $[61, 61, -3w - 7]$ | $\phantom{-}12$ |
71 | $[71, 71, -8w + 7]$ | $-8$ |
71 | $[71, 71, w - 9]$ | $\phantom{-}7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4,2,2]$ | $1$ |
29 | $[29,29,-w + 6]$ | $1$ |