Base field \(\Q(\sqrt{3}, \sqrt{11})\)
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, -w^{3} + 6w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 5x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{7}{2}w - 1]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $\phantom{-}e^{2} - 3$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-e^{3} - e^{2} + 4e + 2$ |
| 11 | $[11, 11, w^{2} + w - 1]$ | $-e^{3} + e^{2} + 4e - 2$ |
| 25 | $[25, 5, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $-e^{3} - 2e^{2} + 6e + 3$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} - w^{2} + \frac{7}{2}w + 4]$ | $\phantom{-}e^{3} - 2e^{2} - 6e + 3$ |
| 37 | $[37, 37, -w^{3} + 7w + 1]$ | $\phantom{-}2e^{3} + e^{2} - 8e - 3$ |
| 37 | $[37, 37, -2w + 1]$ | $-e^{2} - 4e + 1$ |
| 37 | $[37, 37, 2w + 1]$ | $-e^{2} + 4e + 1$ |
| 37 | $[37, 37, -w^{3} + 7w - 1]$ | $-2e^{3} + e^{2} + 8e - 3$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - \frac{9}{2}w + 2]$ | $\phantom{-}e^{3} + e^{2} - 6e - 4$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{9}{2}w + 2]$ | $-e^{3} + e^{2} + 6e - 4$ |
| 83 | $[83, 83, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 2]$ | $\phantom{-}4e^{2} - 2e - 12$ |
| 83 | $[83, 83, w^{2} + w - 5]$ | $\phantom{-}2e^{3} - 10e + 4$ |
| 83 | $[83, 83, w^{2} - w - 5]$ | $\phantom{-}2e^{3} - 10e - 4$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 2]$ | $-4e^{2} - 2e + 12$ |
| 97 | $[97, 97, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 8]$ | $-e^{3} - 2e^{2} + 2e + 3$ |
| 97 | $[97, 97, \frac{5}{2}w^{3} - w^{2} - \frac{31}{2}w + 6]$ | $-5e^{3} + 18e - 9$ |
| 97 | $[97, 97, -\frac{11}{2}w^{3} + 4w^{2} + \frac{71}{2}w - 26]$ | $\phantom{-}5e^{3} - 18e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-\frac{1}{2}w^{3}+\frac{7}{2}w-1]$ | $-1$ |