Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} - w - 7]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 11x^{3} - 2x^{2} + 28x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 3e + 3$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 3e + 3$ |
| 7 | $[7, 7, w^{2} - w - 7]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $-e^{2} - e + 6$ |
| 13 | $[13, 13, -2w - 1]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 3e^{2} - 3e - 1$ |
| 17 | $[17, 17, -2w^{2} + 6w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + e + 9$ |
| 31 | $[31, 31, -2w^{2} + 2w + 19]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 4e^{2} + 5e + 8$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $-e^{2} - e + 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 4e^{2} - 2e + 3$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $-e^{4} + 8e^{2} + e - 10$ |
| 43 | $[43, 43, -2w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 4e - 13$ |
| 43 | $[43, 43, 12w^{2} - 8w - 101]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{7}{2}e^{2} - 5e + 5$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 3e^{2} - 10e + 2$ |
| 59 | $[59, 59, -w^{2} + w + 11]$ | $\phantom{-}2e^{3} + e^{2} - 15e - 6$ |
| 61 | $[61, 61, -w^{2} - w - 1]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + e - 7$ |
| 79 | $[79, 79, -2w^{2} + 4w + 7]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 3e + 14$ |
| 83 | $[83, 83, 2w - 1]$ | $-e^{4} + 3e^{3} + 11e^{2} - 17e - 24$ |
| 89 | $[89, 89, 5w^{2} - 3w - 43]$ | $\phantom{-}\frac{1}{2}e^{4} - 3e^{3} - \frac{13}{2}e^{2} + 18e + 15$ |
| 103 | $[103, 103, -2w + 5]$ | $-e^{4} + 8e^{2} - 3e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} - w - 7]$ | $-1$ |