Base field 5.5.24217.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} - x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 40x^{2} - 80x + 48\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -2w^{4} + w^{3} + 9w^{2} - 2w - 3]$ | $\phantom{-}2$ |
17 | $[17, 17, -2w^{4} + w^{3} + 9w^{2} - 3w - 5]$ | $\phantom{-}e$ |
17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}\frac{1}{8}e^{3} - \frac{3}{4}e^{2} - \frac{5}{2}e + 7$ |
23 | $[23, 23, w^{3} - 3w]$ | $-\frac{1}{8}e^{3} + \frac{1}{4}e^{2} + \frac{9}{2}e + 5$ |
29 | $[29, 29, 2w^{4} - w^{3} - 10w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{3} + e^{2} + 7e - 6$ |
32 | $[32, 2, 2]$ | $-e + 3$ |
37 | $[37, 37, -w^{4} + w^{3} + 4w^{2} - 2w]$ | $-\frac{1}{4}e^{2} + e + 9$ |
41 | $[41, 41, -3w^{4} + 2w^{3} + 14w^{2} - 5w - 7]$ | $\phantom{-}\frac{1}{8}e^{3} - \frac{11}{2}e - 6$ |
43 | $[43, 43, -3w^{4} + w^{3} + 14w^{2} - 3w - 6]$ | $-\frac{1}{8}e^{3} + \frac{7}{2}e + 8$ |
47 | $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ | $-\frac{3}{8}e^{3} + e^{2} + \frac{21}{2}e + 4$ |
53 | $[53, 53, 2w^{4} - w^{3} - 8w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - 5e + 6$ |
53 | $[53, 53, -2w^{4} + w^{3} + 10w^{2} - 4w - 6]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - 9e - 4$ |
59 | $[59, 59, -w^{4} + 4w^{2} + 1]$ | $\phantom{-}\frac{3}{8}e^{3} - \frac{5}{4}e^{2} - \frac{19}{2}e + 3$ |
59 | $[59, 59, -3w^{4} + 2w^{3} + 14w^{2} - 6w - 8]$ | $\phantom{-}\frac{3}{8}e^{3} - \frac{3}{4}e^{2} - \frac{23}{2}e - 7$ |
61 | $[61, 61, 4w^{4} - 2w^{3} - 18w^{2} + 5w + 7]$ | $-\frac{1}{8}e^{3} + \frac{1}{2}e^{2} + \frac{7}{2}e - 4$ |
61 | $[61, 61, 3w^{4} - w^{3} - 15w^{2} + 2w + 7]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 14e$ |
73 | $[73, 73, -4w^{4} + 2w^{3} + 18w^{2} - 7w - 6]$ | $\phantom{-}\frac{3}{4}e^{2} - 3e - 11$ |
83 | $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} - 3e - 8$ |
83 | $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ | $-\frac{3}{8}e^{3} + \frac{7}{4}e^{2} + \frac{19}{2}e - 13$ |
97 | $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ | $\phantom{-}1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$97$ | $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ | $-1$ |