Base field 4.4.7625.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 4x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 21x^{4} + 120x^{2} - 192\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{3}{2}w + 4]$ | $\phantom{-}0$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{4}w^{3} - \frac{3}{4}w^{2} + \frac{5}{4}w + 3]$ | $-\frac{1}{8}e^{4} + \frac{13}{8}e^{2} - 2$ |
| 11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{4}w^{2} + \frac{9}{4}w]$ | $-\frac{1}{8}e^{4} + \frac{21}{8}e^{2} - 7$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{21}{8}e^{2} + 11$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{1}{4}w + 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{17}{4}e^{3} + 13e$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + 3]$ | $-\frac{1}{8}e^{5} + \frac{21}{8}e^{3} - 11e$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} - \frac{1}{4}w^{2} + \frac{19}{4}w + 4]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{55}{8}e^{2} + 24$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} + \frac{7}{4}w^{2} + \frac{11}{4}w - 5]$ | $-\frac{7}{8}e^{4} + \frac{107}{8}e^{2} - 36$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 5]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + 26e$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{13}{8}e^{3} + 2e$ |
| 59 | $[59, 59, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{5}{4}w - 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{13}{8}e^{3} + 2e$ |
| 59 | $[59, 59, w^{2} - 7]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{17}{4}e^{3} + 17e$ |
| 61 | $[61, 61, -\frac{5}{4}w^{3} - \frac{7}{4}w^{2} + \frac{37}{4}w + 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{17}{2}e^{2} + 26$ |
| 71 | $[71, 71, \frac{3}{4}w^{3} + \frac{9}{4}w^{2} - \frac{11}{4}w - 7]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{39}{8}e^{2} + 14$ |
| 71 | $[71, 71, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{13}{4}w - 2]$ | $-\frac{3}{8}e^{4} + \frac{39}{8}e^{2} - 10$ |
| 79 | $[79, 79, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{1}{4}w - 7]$ | $\phantom{-}\frac{3}{8}e^{5} - \frac{47}{8}e^{3} + 15e$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} + \frac{3}{4}w^{2} - \frac{9}{4}w - 2]$ | $-\frac{1}{2}e^{5} + \frac{17}{2}e^{3} - 30e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{7}{8}e^{4} - \frac{123}{8}e^{2} + 48$ |
| 89 | $[89, 89, -w^{2} + 2w + 1]$ | $\phantom{-}2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{3}{2}w + 4]$ | $1$ |