Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[27,3,-w^{3} + 5w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 31x^{2} + 28x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 1]$ | $-\frac{1}{8}e^{3} - \frac{3}{8}e^{2} + 3e - 1$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $-\frac{1}{16}e^{3} - \frac{7}{16}e^{2} + \frac{3}{4}e + 5$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{16}e^{3} + \frac{1}{16}e^{2} + \frac{13}{4}e - 4$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{16}e^{3} + \frac{7}{16}e^{2} - \frac{3}{4}e$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{3}{4}e^{2} - 7e + 4$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $-\frac{5}{16}e^{3} - \frac{19}{16}e^{2} + \frac{35}{4}e + 3$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 3$ |
| 53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{7}{8}e^{2} - \frac{1}{2}e - 8$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 15e + 6$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}\frac{1}{16}e^{3} + \frac{7}{16}e^{2} - \frac{3}{4}e - 3$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{3}{8}e^{3} - \frac{5}{8}e^{2} + \frac{23}{2}e - 9$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{3}{4}e^{2} - 7e - 2$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $-\frac{1}{8}e^{3} + \frac{1}{8}e^{2} + \frac{7}{2}e - 8$ |
| 79 | $[79, 79, w^{2} - 5]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 14e - 1$ |
| 101 | $[101, 101, w^{3} - 6w]$ | $\phantom{-}\frac{5}{16}e^{3} + \frac{19}{16}e^{2} - \frac{35}{4}e - 5$ |
| 101 | $[101, 101, w^{2} - 2w - 4]$ | $-\frac{1}{2}e^{2} - \frac{5}{2}e + 15$ |
| 103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $-\frac{1}{16}e^{3} - \frac{15}{16}e^{2} - \frac{3}{4}e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w^{3} - w^{2} - 5w]$ | $-1$ |
| $9$ | $[9,3,w^{3} - w^{2} - 4w]$ | $-1$ |