Base field 6.6.980125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 60x^{6} + 1252x^{4} - 10848x^{2} + 32768\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $-\frac{1}{64}e^{7} + \frac{3}{4}e^{5} - \frac{171}{16}e^{3} + \frac{91}{2}e$ |
| 11 | $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ | $-\frac{1}{32}e^{5} + \frac{17}{16}e^{3} - \frac{15}{2}e$ |
| 19 | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{3}{256}e^{7} - \frac{35}{64}e^{5} + \frac{471}{64}e^{3} - \frac{229}{8}e$ |
| 29 | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $-1$ |
| 31 | $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $\phantom{-}\frac{7}{512}e^{7} - \frac{81}{128}e^{5} + \frac{1055}{128}e^{3} - \frac{453}{16}e$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $-e^{2} + 14$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ | $-\frac{5}{512}e^{7} + \frac{59}{128}e^{5} - \frac{829}{128}e^{3} + \frac{431}{16}e$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}\frac{1}{128}e^{7} - \frac{3}{8}e^{5} + \frac{163}{32}e^{3} - \frac{73}{4}e$ |
| 59 | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - 8e^{2} + 52$ |
| 59 | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $-\frac{1}{16}e^{6} + \frac{23}{8}e^{4} - 38e^{2} + 148$ |
| 59 | $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{25}{16}e^{4} + 24e^{2} - 112$ |
| 61 | $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ | $-\frac{1}{128}e^{7} + \frac{11}{32}e^{5} - \frac{129}{32}e^{3} + \frac{39}{4}e$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{32}e^{6} + \frac{21}{16}e^{4} - 15e^{2} + 49$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{23}{8}e^{4} + 38e^{2} - 144$ |
| 81 | $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ | $-\frac{23}{512}e^{7} + \frac{273}{128}e^{5} - \frac{3791}{128}e^{3} + \frac{1941}{16}e$ |
| 89 | $[89, 89, -w^{5} + 6w^{3} - 7w]$ | $-\frac{3}{32}e^{6} + \frac{71}{16}e^{4} - \frac{125}{2}e^{2} + 270$ |
| 89 | $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ | $-\frac{3}{256}e^{7} + \frac{33}{64}e^{5} - \frac{403}{64}e^{3} + \frac{161}{8}e$ |
| 101 | $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ | $-\frac{1}{16}e^{6} + \frac{23}{8}e^{4} - \frac{75}{2}e^{2} + 142$ |
| 101 | $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ | $\phantom{-}\frac{7}{256}e^{7} - \frac{83}{64}e^{5} + \frac{1155}{64}e^{3} - \frac{585}{8}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $1$ |