Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[83, 83, 6w - 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e^{2} + e - 3$ |
| 11 | $[11, 11, -2w + 1]$ | $\phantom{-}e^{2} + e - 4$ |
| 11 | $[11, 11, 2w + 1]$ | $-4e^{2} - 7e + 3$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}2e^{2} + 5e - 3$ |
| 13 | $[13, 13, -w + 4]$ | $-2e^{2} - 4e - 1$ |
| 23 | $[23, 23, -3w + 2]$ | $-e^{2} - 1$ |
| 23 | $[23, 23, 3w + 2]$ | $\phantom{-}e$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}5e^{2} + 9e - 6$ |
| 37 | $[37, 37, 2w - 7]$ | $\phantom{-}3e^{2} + 7e - 3$ |
| 37 | $[37, 37, -2w - 7]$ | $-e^{2} - 2e - 1$ |
| 47 | $[47, 47, -4w - 1]$ | $\phantom{-}5e^{2} + 3e - 7$ |
| 47 | $[47, 47, 4w - 1]$ | $-2e^{2} - 5e - 3$ |
| 49 | $[49, 7, -7]$ | $-e^{2} - 7e - 4$ |
| 59 | $[59, 59, 5w - 4]$ | $\phantom{-}3e^{2} + 4e - 5$ |
| 59 | $[59, 59, -5w - 4]$ | $-e^{2} - 2e - 8$ |
| 61 | $[61, 61, -w - 8]$ | $\phantom{-}e^{2} - 3e - 5$ |
| 61 | $[61, 61, w - 8]$ | $-e - 4$ |
| 71 | $[71, 71, 5w - 2]$ | $-2e^{2} + 6e + 13$ |
| 71 | $[71, 71, -5w - 2]$ | $\phantom{-}2e^{2} + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $83$ | $[83, 83, 6w - 5]$ | $-1$ |