Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 2, w^{2} - w - 7]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 9x^{3} + 4x^{2} + 20x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{5}{2}e^{2} - \frac{7}{2}e - \frac{5}{2}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - \frac{5}{2}e^{2} + \frac{17}{2}e + \frac{11}{2}$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{3}{2}e^{2} - \frac{3}{2}e + \frac{7}{2}$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{2}e^{4} + 2e^{3} + \frac{1}{2}e^{2} - \frac{15}{2}e + \frac{5}{2}$ |
| 13 | $[13, 13, -2w + 1]$ | $-e^{4} + 2e^{3} + 6e^{2} - 7e - 7$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - \frac{3}{2}e^{2} + \frac{13}{2}e - \frac{3}{2}$ |
| 25 | $[25, 5, w^{2} - 7]$ | $-\frac{1}{2}e^{4} + 3e^{3} - \frac{1}{2}e^{2} - \frac{25}{2}e + \frac{11}{2}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{7}{2}e^{2} + \frac{7}{2}e + \frac{5}{2}$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{7}{2}e^{2} - \frac{13}{2}e + \frac{5}{2}$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $\phantom{-}e^{4} - e^{3} - 6e^{2} + 5e + 6$ |
| 41 | $[41, 41, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - \frac{9}{2}e^{2} - \frac{21}{2}e + \frac{7}{2}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{3}{2}e^{4} + 2e^{3} + \frac{17}{2}e^{2} - \frac{15}{2}e - \frac{7}{2}$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{4} + 3e^{3} - \frac{1}{2}e^{2} - \frac{23}{2}e + \frac{7}{2}$ |
| 59 | $[59, 59, 2w - 3]$ | $\phantom{-}e^{4} - 3e^{3} - 2e^{2} + 12e - 8$ |
| 67 | $[67, 67, w - 5]$ | $-e^{3} + e^{2} + e + 1$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $-e^{4} + 3e^{3} + 5e^{2} - 16e - 3$ |
| 73 | $[73, 73, w^{2} + 1]$ | $-e^{3} - e^{2} + 3e + 13$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $-e^{4} - e^{3} + 9e^{2} + 2e - 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{2} - w - 7]$ | $-1$ |