Base field 5.5.138136.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[8, 4, w^{4} - 7w^{2} - 2w + 6]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 22x^{2} - 16x + 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
7 | $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{5}{2}e + 9$ |
19 | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $-\frac{1}{2}e^{3} + e^{2} + 7e - 4$ |
19 | $[19, 19, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{1}{2}e^{3} + e^{2} + 7e - 4$ |
29 | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $-\frac{1}{4}e^{3} + \frac{9}{2}e + 2$ |
31 | $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ | $-\frac{1}{2}e^{3} + 2e^{2} + 6e - 16$ |
37 | $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{7}{2}e + 10$ |
53 | $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{3}{2}e + 10$ |
59 | $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 7e + 4$ |
61 | $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ | $-\frac{3}{4}e^{3} + 3e^{2} + \frac{19}{2}e - 22$ |
61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{11}{2}e + 2$ |
61 | $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ | $\phantom{-}6$ |
67 | $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 6e + 4$ |
67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{3} + e^{2} + 5e - 4$ |
71 | $[71, 71, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - 7e + 16$ |
73 | $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{11}{2}e - 2$ |
79 | $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ | $-\frac{1}{2}e^{3} + e^{2} + 6e$ |
83 | $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 9e - 4$ |
97 | $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{2}e - 10$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.