Base field 4.4.1957.1
Generator \(w\), with minimal polynomial \(x^4 - 4 x^2 - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[57, 57, -w^3 + 2 w^2 + 3 w - 4]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^3 + 3 w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^2 + 2]$ | $-2$ |
| 16 | $[16, 2, 2]$ | $-5$ |
| 19 | $[19, 19, -w^3 + w^2 + 4 w]$ | $-1$ |
| 23 | $[23, 23, w^3 + w^2 - 4 w - 2]$ | $\phantom{-}0$ |
| 27 | $[27, 3, -2 w^3 + w^2 + 6 w - 1]$ | $\phantom{-}8$ |
| 31 | $[31, 31, -w^3 + 5 w]$ | $-4$ |
| 37 | $[37, 37, -w^3 + 5 w + 1]$ | $-2$ |
| 43 | $[43, 43, w^2 + w - 3]$ | $\phantom{-}2$ |
| 43 | $[43, 43, -w^2 + 2 w + 3]$ | $\phantom{-}10$ |
| 47 | $[47, 47, -w^3 + w^2 + 2 w + 2]$ | $\phantom{-}12$ |
| 47 | $[47, 47, 3 w^3 - w^2 - 10 w - 2]$ | $\phantom{-}0$ |
| 53 | $[53, 53, -w^3 + w^2 + 2 w - 3]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -2 w^3 + w^2 + 8 w + 1]$ | $-6$ |
| 59 | $[59, 59, w^3 - 2 w^2 - 3 w + 3]$ | $\phantom{-}6$ |
| 61 | $[61, 61, -w^3 + w^2 + w - 2]$ | $-14$ |
| 67 | $[67, 67, 2 w^3 - 5 w - 2]$ | $\phantom{-}14$ |
| 71 | $[71, 71, 2 w^2 - w - 3]$ | $\phantom{-}12$ |
| 73 | $[73, 73, 2 w^2 - w - 5]$ | $-2$ |
| 73 | $[73, 73, w^3 - 2 w^2 - 2 w + 5]$ | $\phantom{-}14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^3 + 3 w + 1]$ | $1$ |
| $19$ | $[19, 19, -w^3 + w^2 + 4 w]$ | $1$ |