Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 32x^{6} + 318x^{4} - 1216x^{2} + 1536\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $-\frac{7}{256}e^{7} + \frac{13}{16}e^{5} - \frac{857}{128}e^{3} + \frac{123}{8}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{5}{2}e^{4} + \frac{269}{16}e^{2} - 29$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{7}{256}e^{7} - \frac{13}{16}e^{5} + \frac{857}{128}e^{3} - \frac{115}{8}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{5}{2}e^{4} + \frac{253}{16}e^{2} - 21$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{2}e^{4} - \frac{17}{16}e^{2} + 12$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-\frac{31}{256}e^{7} + \frac{53}{16}e^{5} - \frac{3009}{128}e^{3} + \frac{371}{8}e$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}\frac{5}{256}e^{7} - \frac{7}{16}e^{5} + \frac{155}{128}e^{3} + \frac{47}{8}e$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $-\frac{25}{256}e^{7} + \frac{43}{16}e^{5} - \frac{2439}{128}e^{3} + \frac{277}{8}e$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{16}e^{6} - 2e^{4} + \frac{143}{8}e^{2} - 38$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $-\frac{3}{128}e^{7} + \frac{5}{8}e^{5} - \frac{285}{64}e^{3} + \frac{39}{4}e$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $\phantom{-}\frac{5}{64}e^{7} - \frac{9}{4}e^{5} + \frac{571}{32}e^{3} - \frac{83}{2}e$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $-\frac{9}{128}e^{7} + \frac{15}{8}e^{5} - \frac{791}{64}e^{3} + \frac{77}{4}e$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{7}{256}e^{7} - \frac{13}{16}e^{5} + \frac{857}{128}e^{3} - \frac{123}{8}e$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $\phantom{-}\frac{5}{256}e^{7} - \frac{7}{16}e^{5} + \frac{155}{128}e^{3} + \frac{39}{8}e$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $-\frac{7}{64}e^{7} + \frac{11}{4}e^{5} - \frac{505}{32}e^{3} + \frac{33}{2}e$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{1}{256}e^{7} + \frac{3}{16}e^{5} - \frac{287}{128}e^{3} + \frac{29}{8}e$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $\phantom{-}\frac{63}{256}e^{7} - \frac{109}{16}e^{5} + \frac{6305}{128}e^{3} - \frac{779}{8}e$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $-\frac{7}{16}e^{6} + 12e^{4} - \frac{681}{8}e^{2} + 162$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,w^{4}-2w^{3}-4w^{2}+6w+1]$ | $-1$ |