Base field \(\Q(\sqrt{14}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[31, 31, 2w - 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}e^{2} - e - 2$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e^{2} - e - 2$ |
| 7 | $[7, 7, -2w - 7]$ | $\phantom{-}2$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{2} - 2e - 3$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}e^{2} - 2e - 1$ |
| 11 | $[11, 11, -w + 5]$ | $\phantom{-}2e^{2} - 6$ |
| 13 | $[13, 13, -w - 1]$ | $\phantom{-}2e^{2} + e - 5$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}e^{2} - e$ |
| 31 | $[31, 31, 2w - 5]$ | $-1$ |
| 31 | $[31, 31, -2w - 5]$ | $-4e^{2} + 2e + 8$ |
| 43 | $[43, 43, 7w + 27]$ | $\phantom{-}3e^{2} - 2e - 7$ |
| 43 | $[43, 43, 3w + 13]$ | $\phantom{-}2e^{2} - 4e - 2$ |
| 47 | $[47, 47, 2w - 3]$ | $-4e + 4$ |
| 47 | $[47, 47, -2w - 3]$ | $\phantom{-}2e^{2} - 6$ |
| 61 | $[61, 61, 7w + 25]$ | $-e^{2} - e$ |
| 61 | $[61, 61, -5w - 17]$ | $-2e^{2} + 3e + 7$ |
| 67 | $[67, 67, -w - 9]$ | $-e^{2} + 4e - 5$ |
| 67 | $[67, 67, w - 9]$ | $\phantom{-}3e^{2} - 4e + 3$ |
| 101 | $[101, 101, 3w - 5]$ | $\phantom{-}4e^{2} - 3e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, 2w - 5]$ | $1$ |