Base field 3.3.404.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[36, 6, -w^{2} + 5]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
3 | $[3, 3, w^{2} - 2w - 2]$ | $\phantom{-}0$ |
7 | $[7, 7, -w + 2]$ | $-4$ |
9 | $[9, 3, w^{2} - 2]$ | $-1$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $-4$ |
29 | $[29, 29, -2w + 1]$ | $\phantom{-}6$ |
37 | $[37, 37, 2w^{2} - 4w - 3]$ | $-6$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}6$ |
37 | $[37, 37, 2w^{2} - w - 8]$ | $-6$ |
41 | $[41, 41, w^{2} - 4w + 2]$ | $\phantom{-}2$ |
43 | $[43, 43, -2w^{2} + 2w + 7]$ | $-4$ |
43 | $[43, 43, -2w^{2} + 3w + 6]$ | $\phantom{-}8$ |
43 | $[43, 43, -w^{2} + 6]$ | $\phantom{-}12$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}10$ |
53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-6$ |
59 | $[59, 59, 2w - 3]$ | $\phantom{-}4$ |
61 | $[61, 61, -w - 4]$ | $\phantom{-}2$ |
67 | $[67, 67, -2w^{2} - w + 2]$ | $\phantom{-}12$ |
73 | $[73, 73, 2w^{2} - 3w - 12]$ | $\phantom{-}14$ |
83 | $[83, 83, -2w - 5]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 1]$ | $-1$ |
$9$ | $[9, 3, w^{2} - 2]$ | $1$ |