Base field 4.4.5125.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 6 x^2 + 7 x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41, 41, 3 w^2 - 2 w - 10]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^2 + 2 w + 3]$ | $-1$ |
| 9 | $[9, 3, w^3 - 3 w^2 - 2 w + 9]$ | $\phantom{-}4$ |
| 9 | $[9, 3, -w^3 + 5 w + 5]$ | $\phantom{-}4$ |
| 11 | $[11, 11, w]$ | $\phantom{-}5$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}5$ |
| 16 | $[16, 2, 2]$ | $-4$ |
| 19 | $[19, 19, -w^3 + 2 w^2 + 3 w - 2]$ | $-6$ |
| 19 | $[19, 19, w^3 - w^2 - 4 w + 2]$ | $-6$ |
| 29 | $[29, 29, w^3 - 4 w^2 - w + 10]$ | $-2$ |
| 29 | $[29, 29, -w^3 + 3 w^2 + w - 7]$ | $-2$ |
| 41 | $[41, 41, 3 w^2 - 2 w - 10]$ | $-1$ |
| 49 | $[49, 7, -2 w^2 + 3 w + 8]$ | $\phantom{-}6$ |
| 49 | $[49, 7, w^3 - 2 w^2 - 2 w + 5]$ | $\phantom{-}6$ |
| 71 | $[71, 71, -w - 3]$ | $\phantom{-}9$ |
| 71 | $[71, 71, w - 4]$ | $\phantom{-}9$ |
| 79 | $[79, 79, -w^3 + w^2 + 3 w + 3]$ | $\phantom{-}4$ |
| 79 | $[79, 79, -w^3 + 2 w^2 + 2 w - 6]$ | $\phantom{-}4$ |
| 89 | $[89, 89, w^3 - 3 w^2 - 3 w + 7]$ | $\phantom{-}8$ |
| 89 | $[89, 89, w^3 - 6 w - 2]$ | $\phantom{-}8$ |
| 101 | $[101, 101, 2 w^3 - 5 w^2 - 3 w + 9]$ | $\phantom{-}11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 3 w^2 - 2 w - 10]$ | $1$ |