Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[16, 4, -2w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 18x^{4} + 36x^{2} - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 5 | $[5, 5, -w + 2]$ | $-\frac{1}{4}e^{4} + \frac{9}{2}e^{2} - 5$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{3}{8}e^{5} + \frac{25}{4}e^{3} - \frac{13}{2}e$ |
| 11 | $[11, 11, 2w - 1]$ | $-\frac{3}{8}e^{5} + \frac{25}{4}e^{3} - \frac{9}{2}e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-\frac{5}{8}e^{5} + \frac{43}{4}e^{3} - \frac{25}{2}e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{25}{2}e^{2} + 9$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{11}{4}e^{3} + \frac{21}{2}e$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $\phantom{-}e^{4} - 17e^{2} + 18$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-\frac{3}{4}e^{5} + \frac{25}{2}e^{3} - 10e$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $-\frac{3}{4}e^{5} + \frac{25}{2}e^{3} - 11e$ |
| 47 | $[47, 47, -w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - 9e^{2} + 14$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{25}{2}e^{3} + 8e$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{25}{2}e^{3} + 11e$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $-\frac{1}{4}e^{4} + \frac{9}{2}e^{2} + 3$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}\frac{7}{4}e^{4} - \frac{57}{2}e^{2} + 25$ |
| 79 | $[79, 79, 2w + 3]$ | $-\frac{5}{4}e^{5} + \frac{43}{2}e^{3} - 27e$ |
| 89 | $[89, 89, 2w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{9}{2}e^{2} + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 1]$ | $-1$ |