Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ |
| 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:
| \(x^{8} - x^{7} - 18x^{6} + 19x^{5} + 91x^{4} - 76x^{3} - 152x^{2} + 64x + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $-\frac{1}{8}e^{7} + \frac{15}{8}e^{5} - \frac{5}{8}e^{4} - \frac{27}{4}e^{3} + \frac{21}{8}e^{2} + 5e - 1$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $\phantom{-}\frac{3}{16}e^{7} + \frac{3}{16}e^{6} - \frac{11}{4}e^{5} - \frac{19}{16}e^{4} + \frac{179}{16}e^{3} - \frac{1}{8}e^{2} - 13e + 3$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{3}{16}e^{7} + \frac{7}{16}e^{6} - \frac{5}{2}e^{5} - \frac{83}{16}e^{4} + \frac{143}{16}e^{3} + \frac{137}{8}e^{2} - \frac{19}{2}e - 10$ |
| 29 | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $\phantom{-}1$ |
| 32 | $[32, 2, 2]$ | $-\frac{3}{16}e^{7} - \frac{5}{16}e^{6} + \frac{23}{8}e^{5} + \frac{55}{16}e^{4} - \frac{201}{16}e^{3} - \frac{41}{4}e^{2} + \frac{25}{2}e + 9$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{1}{8}e^{7} - \frac{3}{8}e^{6} + \frac{7}{4}e^{5} + \frac{37}{8}e^{4} - \frac{63}{8}e^{3} - 15e^{2} + 12e + 12$ |
| 41 | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $-\frac{3}{16}e^{7} - \frac{3}{16}e^{6} + \frac{11}{4}e^{5} + \frac{19}{16}e^{4} - \frac{179}{16}e^{3} - \frac{7}{8}e^{2} + 14e + 1$ |
| 43 | $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ | $\phantom{-}\frac{9}{16}e^{7} + \frac{5}{16}e^{6} - 8e^{5} - \frac{17}{16}e^{4} + \frac{429}{16}e^{3} - \frac{1}{8}e^{2} - 16e + 2$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ | $-\frac{1}{16}e^{7} + \frac{3}{16}e^{6} + e^{5} - \frac{55}{16}e^{4} - \frac{53}{16}e^{3} + \frac{121}{8}e^{2} + e - 14$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $-\frac{1}{8}e^{7} + \frac{3}{8}e^{6} + 2e^{5} - \frac{47}{8}e^{4} - \frac{53}{8}e^{3} + \frac{73}{4}e^{2} + 5e - 6$ |
| 61 | $[61, 61, w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{1}{2}e^{6} - \frac{13}{4}e^{5} - \frac{19}{4}e^{4} + 10e^{3} + \frac{33}{4}e^{2} - e + 4$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ | $\phantom{-}\frac{5}{16}e^{7} + \frac{9}{16}e^{6} - 4e^{5} - \frac{85}{16}e^{4} + \frac{209}{16}e^{3} + \frac{91}{8}e^{2} - \frac{23}{2}e - 2$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $-\frac{3}{16}e^{7} + \frac{1}{16}e^{6} + \frac{5}{2}e^{5} - \frac{37}{16}e^{4} - \frac{119}{16}e^{3} + \frac{71}{8}e^{2} + 7e - 3$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ | $-\frac{1}{16}e^{7} + \frac{3}{16}e^{6} + \frac{1}{2}e^{5} - \frac{63}{16}e^{4} + \frac{27}{16}e^{3} + \frac{133}{8}e^{2} - \frac{15}{2}e - 10$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{5}{8}e^{6} - \frac{23}{8}e^{5} - \frac{13}{2}e^{4} + \frac{59}{8}e^{3} + \frac{137}{8}e^{2} - 5e - 7$ |
| 71 | $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ | $-\frac{3}{8}e^{7} - \frac{5}{8}e^{6} + \frac{19}{4}e^{5} + \frac{47}{8}e^{4} - \frac{113}{8}e^{3} - \frac{29}{2}e^{2} + 8e + 12$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ | $\phantom{-}\frac{1}{16}e^{7} + \frac{1}{16}e^{6} - \frac{3}{4}e^{5} + \frac{7}{16}e^{4} + \frac{33}{16}e^{3} - \frac{63}{8}e^{2} - \frac{3}{2}e + 10$ |
| 81 | $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ | $-\frac{1}{4}e^{7} - \frac{1}{4}e^{6} + 3e^{5} + \frac{1}{4}e^{4} - \frac{29}{4}e^{3} + \frac{21}{2}e^{2} - e - 14$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ | $-\frac{1}{8}e^{7} - \frac{5}{8}e^{6} + \frac{49}{8}e^{4} + \frac{91}{8}e^{3} - \frac{55}{4}e^{2} - 26e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $-1$ |