Base field 3.3.993.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[21, 21, w^{2} - 2w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 6x^{2} + 4x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e^{2} - 2$ |
| 7 | $[7, 7, w + 1]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-e^{3} + e^{2} + 4e - 3$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $-2e^{2} + 2e + 6$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}2$ |
| 25 | $[25, 5, -w^{2} - w + 4]$ | $-e^{3} + 3e + 4$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}2e^{2} - e - 6$ |
| 31 | $[31, 31, 2w^{2} - w - 14]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 6$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-e^{3} + 2e^{2} + 4e - 6$ |
| 37 | $[37, 37, -3w^{2} + w + 19]$ | $-3e^{3} + 13e + 2$ |
| 49 | $[49, 7, w^{2} - 2w - 4]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 2$ |
| 53 | $[53, 53, -w - 4]$ | $\phantom{-}e^{3} + 4e^{2} - 4e - 12$ |
| 61 | $[61, 61, 2w^{2} + w - 7]$ | $\phantom{-}e^{3} - 2e^{2} - 6e + 8$ |
| 71 | $[71, 71, 2w^{2} - 2w - 13]$ | $\phantom{-}2e^{2} + 2e - 12$ |
| 73 | $[73, 73, w - 5]$ | $-3e^{3} - 2e^{2} + 10e + 12$ |
| 83 | $[83, 83, w^{2} - 3w - 2]$ | $-e^{3} - e^{2} + 4e + 6$ |
| 89 | $[89, 89, w^{2} + 2w - 4]$ | $-2e^{3} - 2e^{2} + 10e + 2$ |
| 97 | $[97, 97, -w^{2} + 2w + 7]$ | $\phantom{-}e^{3} - 3e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w]$ | $-1$ |
| $7$ | $[7, 7, w + 1]$ | $1$ |