Base field 4.4.12357.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[21, 21, -w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $\phantom{-}2e^{3} - 7e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{2} - 5$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-4e^{3} + 12e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}3e^{2} - 10$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 4]$ | $-3e^{3} + 9e$ |
| 31 | $[31, 31, w^{3} - w^{2} - 3w + 1]$ | $-6e^{2} + 14$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $\phantom{-}5e^{3} - 17e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}4e^{2} - 10$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}2e^{3} - 8e$ |
| 53 | $[53, 53, -w^{2} - w + 4]$ | $-5e^{3} + 13e$ |
| 59 | $[59, 59, -w^{3} + 4w - 2]$ | $\phantom{-}5e^{3} - 18e$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ | $-8e^{2} + 14$ |
| 89 | $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ | $\phantom{-}2e^{3} - e$ |
| 89 | $[89, 89, w^{3} - 5w + 1]$ | $-4e^{3} + 20e$ |
| 97 | $[97, 97, w^{3} - 6w - 1]$ | $-3e^{2} + 8$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ | $\phantom{-}e^{2} - 12$ |
| 101 | $[101, 101, -w^{3} + 6w - 2]$ | $-e^{3} + e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |
| $7$ | $[7, 7, -w^{2} + 2]$ | $-1$ |