Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $4$ |
| CM: | yes |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} - 44x^{2} - 176x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 5]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $-\frac{1}{44}e^{3} - \frac{3}{11}e^{2} + \frac{9}{11}e + \frac{72}{11}$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $-\frac{3}{44}e^{3} + \frac{2}{11}e^{2} + \frac{27}{11}e - \frac{48}{11}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{11}e^{3} + \frac{1}{11}e^{2} - \frac{47}{11}e - \frac{68}{11}$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $\phantom{-}\frac{1}{44}e^{3} + \frac{3}{11}e^{2} + \frac{2}{11}e - \frac{138}{11}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $-\frac{5}{44}e^{3} - \frac{4}{11}e^{2} + \frac{56}{11}e + \frac{74}{11}$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $-\frac{3}{44}e^{3} + \frac{2}{11}e^{2} + \frac{16}{11}e - \frac{114}{11}$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $\phantom{-}\frac{7}{44}e^{3} - \frac{1}{11}e^{2} - \frac{74}{11}e - \frac{86}{11}$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $\phantom{-}0$ |
| 79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $\phantom{-}0$ |
| 81 | $[81, 3, -3]$ | $-6$ |
| 109 | $[109, 109, w^{2} - w - 7]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $-1$ |