Base field 4.4.13025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 3x + 29\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 14x^{3} + 40x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ | $-1$ |
| 4 | $[4, 2, -w^{2} + w + 8]$ | $-1$ |
| 5 | $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ | $\phantom{-}e$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ | $\phantom{-}e$ |
| 19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{7}{2}e^{2} - \frac{7}{2}e$ |
| 19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{7}{2}e^{2} - \frac{7}{2}e$ |
| 29 | $[29, 29, w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 7$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + 7e^{2} - 18e$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 7$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + 7e^{2} - 18e$ |
| 41 | $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ | $-\frac{3}{4}e^{4} + \frac{7}{4}e^{3} + \frac{21}{2}e^{2} - \frac{49}{2}e$ |
| 41 | $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ | $-\frac{3}{4}e^{4} + \frac{7}{4}e^{3} + \frac{21}{2}e^{2} - \frac{49}{2}e$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 6e^{2} + 20e - 6$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 6e^{2} + 20e - 6$ |
| 79 | $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 7$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 7$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + 7e^{2} - 21e + 10$ |
| 89 | $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{11}{4}e^{3} - \frac{23}{2}e^{2} + \frac{75}{2}e + 6$ |
| 89 | $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{11}{4}e^{3} - \frac{23}{2}e^{2} + \frac{75}{2}e + 6$ |
| 109 | $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ | $-\frac{3}{2}e^{4} + \frac{9}{2}e^{3} + 21e^{2} - 59e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ | $1$ |
| $4$ | $[4, 2, -w^{2} + w + 8]$ | $1$ |