Base field 3.3.169.1
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 4 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[64, 4, 4]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^2 + 2 w + 3]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -w^2 + w + 2]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -w + 1]$ | $\phantom{-}2$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}0$ |
| 13 | $[13, 13, -w^2 + 3]$ | $-2$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -2 w^2 + 3 w + 3]$ | $-8$ |
| 31 | $[31, 31, -w^2 + 5]$ | $-8$ |
| 31 | $[31, 31, -w^2 + 3 w + 4]$ | $-8$ |
| 47 | $[47, 47, 2 w - 3]$ | $\phantom{-}4$ |
| 47 | $[47, 47, 2 w^2 - 4 w - 7]$ | $\phantom{-}4$ |
| 47 | $[47, 47, 2 w^2 - 2 w - 3]$ | $\phantom{-}4$ |
| 53 | $[53, 53, 3 w^2 - 4 w - 8]$ | $-6$ |
| 53 | $[53, 53, 4 w^2 - 6 w - 11]$ | $-6$ |
| 53 | $[53, 53, 3 w^2 - 5 w - 6]$ | $-6$ |
| 73 | $[73, 73, w^2 - 4 w - 4]$ | $\phantom{-}14$ |
| 73 | $[73, 73, 2 w^2 - w - 8]$ | $\phantom{-}14$ |
| 73 | $[73, 73, 3 w^2 - 5 w - 5]$ | $\phantom{-}14$ |
| 79 | $[79, 79, -3 w^2 + 5 w + 4]$ | $-4$ |
| 79 | $[79, 79, 2 w^2 - w - 9]$ | $-4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |