Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 14x^{2} + 22x + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $\phantom{-}1$ |
| 8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{11}{4}e + \frac{1}{4}$ |
| 11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{7}{4}e - \frac{7}{4}$ |
| 13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $\phantom{-}e - 1$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{4}e^{2} - \frac{7}{4}e - \frac{9}{4}$ |
| 23 | $[23, 23, -w + 2]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - \frac{7}{2}$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + \frac{15}{4}e + \frac{13}{4}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{3}{4}e^{2} - \frac{15}{4}e - \frac{29}{4}$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{15}{2}e + \frac{1}{2}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + \frac{13}{2}e + \frac{23}{2}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $\phantom{-}e^{3} - 10e - 1$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e + \frac{3}{2}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{19}{2}$ |
| 71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{7}{4}e^{2} - \frac{15}{4}e - \frac{57}{4}$ |
| 71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $\phantom{-}2$ |
| 73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $\phantom{-}e^{2} - 11$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $\phantom{-}e^{2} - 5$ |
| 83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $-e^{2} + 2e + 19$ |
| 89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{17}{2}e - \frac{5}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $-1$ |