Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 20x^{4} + 126x^{2} - 242\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{1}{11}e^{5} - \frac{9}{11}e^{3} + \frac{5}{11}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}2$ |
| 7 | $[7, 7, -w^{3} + 5w - 2]$ | $-\frac{1}{11}e^{5} + \frac{20}{11}e^{3} - \frac{82}{11}e$ |
| 13 | $[13, 13, -w^{3} + 5w + 1]$ | $-\frac{1}{11}e^{5} + \frac{20}{11}e^{3} - \frac{82}{11}e$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 29 | $[29, 29, w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}\frac{3}{11}e^{5} - \frac{38}{11}e^{3} + \frac{92}{11}e$ |
| 31 | $[31, 31, -w^{3} + 4w - 1]$ | $\phantom{-}\frac{2}{11}e^{5} - \frac{18}{11}e^{3} + \frac{10}{11}e$ |
| 41 | $[41, 41, w^{3} - 6w + 1]$ | $-e^{5} + 11e^{3} - 23e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 6w - 1]$ | $-\frac{12}{11}e^{5} + \frac{152}{11}e^{3} - \frac{423}{11}e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ | $-4e^{4} + 48e^{2} - 122$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $\phantom{-}\frac{7}{11}e^{5} - \frac{85}{11}e^{3} + \frac{211}{11}e$ |
| 59 | $[59, 59, w^{3} - w^{2} - 6w + 4]$ | $-\frac{14}{11}e^{5} + \frac{170}{11}e^{3} - \frac{455}{11}e$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-2e^{4} + 26e^{2} - 72$ |
| 67 | $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ | $\phantom{-}\frac{7}{11}e^{5} - \frac{85}{11}e^{3} + \frac{211}{11}e$ |
| 71 | $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ | $-2e$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}\frac{19}{11}e^{5} - \frac{248}{11}e^{3} + \frac{744}{11}e$ |
| 73 | $[73, 73, w^{3} - 6w + 4]$ | $-\frac{12}{11}e^{5} + \frac{152}{11}e^{3} - \frac{423}{11}e$ |
| 83 | $[83, 83, w^{3} - w^{2} - 3w + 4]$ | $-e^{4} + 10e^{2} - 16$ |
| 103 | $[103, 103, w^{3} + w^{2} - 4w - 5]$ | $-2e^{4} + 24e^{2} - 70$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |