Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 8x^{3} - 4x^{2} + 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $\phantom{-}0$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $\phantom{-}2e^{4} - 15e^{2} - 8e + 7$ |
| 9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $-e^{4} + 7e^{2} + 5e - 1$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $-2e^{4} - 2e^{3} + 18e^{2} + 21e - 11$ |
| 11 | $[11, 11, -w - 3]$ | $-e^{4} + 7e^{2} + 6e$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $\phantom{-}e^{4} + e^{3} - 10e^{2} - 9e + 9$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}e^{4} - e^{3} - 6e^{2} + e + 5$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $\phantom{-}e^{4} - 8e^{2} - 7e + 8$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $-2e^{4} + 15e^{2} + 8e - 5$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $-3e^{4} + e^{3} + 22e^{2} + 10e - 10$ |
| 31 | $[31, 31, -w + 3]$ | $\phantom{-}4e^{4} - 30e^{2} - 19e + 11$ |
| 31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $-e^{4} - e^{3} + 7e^{2} + 11e$ |
| 59 | $[59, 59, 2w^{2} - w - 13]$ | $-e^{3} + e^{2} + 5e - 11$ |
| 59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $\phantom{-}e + 5$ |
| 61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 24e + 2$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $-4e^{4} + 30e^{2} + 22e - 10$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $\phantom{-}3e^{4} - 22e^{2} - 14e + 9$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $\phantom{-}2e^{4} - 16e^{2} - 10e + 12$ |
| 79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $\phantom{-}2e^{4} + e^{3} - 17e^{2} - 13e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ | $1$ |