Base field 4.4.3981.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 4 x^2 + 2 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $1$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $-2$ |
| 5 | $[5, 5, w^3 - w^2 - 3 w + 1]$ | $-3$ |
| 9 | $[9, 3, -w^2 + 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^3 + w^2 + 4 w]$ | $\phantom{-}5$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 23 | $[23, 23, w^2 - 2 w - 2]$ | $\phantom{-}6$ |
| 37 | $[37, 37, w^3 - 4 w + 1]$ | $\phantom{-}11$ |
| 37 | $[37, 37, w^3 - w^2 - 5 w + 1]$ | $-7$ |
| 41 | $[41, 41, w^3 - 5 w + 1]$ | $-3$ |
| 43 | $[43, 43, 2 w^3 - w^2 - 7 w]$ | $\phantom{-}8$ |
| 53 | $[53, 53, 2 w - 3]$ | $-9$ |
| 59 | $[59, 59, -2 w^3 + w^2 + 9 w - 1]$ | $\phantom{-}6$ |
| 67 | $[67, 67, -w - 3]$ | $\phantom{-}14$ |
| 67 | $[67, 67, w^3 + w^2 - 5 w - 4]$ | $-4$ |
| 71 | $[71, 71, 2 w^3 - 3 w^2 - 7 w + 5]$ | $\phantom{-}0$ |
| 73 | $[73, 73, w^3 - 6 w]$ | $-7$ |
| 73 | $[73, 73, -w^3 - w^2 + 5 w + 3]$ | $-7$ |
| 79 | $[79, 79, w^3 - 3 w - 4]$ | $-10$ |
| 83 | $[83, 83, w^3 - 2 w^2 - 3 w + 1]$ | $-6$ |
| 83 | $[83, 83, -2 w^3 + 2 w^2 + 6 w - 3]$ | $\phantom{-}12$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).