Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 6x^{7} + 2x^{6} + 44x^{5} - 60x^{4} - 73x^{3} + 147x^{2} - 16x - 38\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{2}{3}e^{4} - \frac{8}{3}e^{3} + \frac{11}{3}e^{2} + \frac{14}{3}e - \frac{5}{3}$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{4}{3}e^{6} - \frac{5}{3}e^{5} + \frac{31}{3}e^{4} - 2e^{3} - 20e^{2} + \frac{37}{3}e + \frac{19}{3}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{2}{3}e^{7} - 3e^{6} - 3e^{5} + \frac{73}{3}e^{4} - 4e^{3} - 54e^{2} + 18e + \frac{71}{3}$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $-\frac{1}{3}e^{7} + \frac{4}{3}e^{6} + 2e^{5} - 10e^{4} - \frac{8}{3}e^{3} + \frac{53}{3}e^{2} + \frac{1}{3}e - 2$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{2}{3}e^{7} - 3e^{6} - \frac{11}{3}e^{5} + 27e^{4} - \frac{8}{3}e^{3} - 66e^{2} + 24e + \frac{88}{3}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{2}{3}e^{7} + \frac{10}{3}e^{6} + 2e^{5} - 27e^{4} + \frac{34}{3}e^{3} + \frac{178}{3}e^{2} - 31e - \frac{56}{3}$ |
| 32 | $[32, 2, 2]$ | $-e^{7} + 4e^{6} + \frac{19}{3}e^{5} - \frac{104}{3}e^{4} - \frac{8}{3}e^{3} + \frac{242}{3}e^{2} - \frac{73}{3}e - \frac{95}{3}$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{5}{3}e^{7} + \frac{23}{3}e^{6} + 7e^{5} - 62e^{4} + \frac{44}{3}e^{3} + \frac{403}{3}e^{2} - \frac{178}{3}e - 48$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{10}{3}e^{6} - \frac{8}{3}e^{5} + 28e^{4} - 6e^{3} - 66e^{2} + \frac{67}{3}e + \frac{101}{3}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{1}{3}e^{5} - \frac{14}{3}e^{4} + 4e^{3} + 15e^{2} - \frac{31}{3}e - 2$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{8}{3}e^{6} - \frac{11}{3}e^{5} + \frac{61}{3}e^{4} + \frac{5}{3}e^{3} - \frac{113}{3}e^{2} + 6e + \frac{22}{3}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}2e^{7} - 9e^{6} - 9e^{5} + \frac{221}{3}e^{4} - 15e^{3} - \frac{490}{3}e^{2} + \frac{206}{3}e + \frac{185}{3}$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{2}{3}e^{6} - \frac{10}{3}e^{5} + \frac{11}{3}e^{4} + 12e^{3} - \frac{7}{3}e^{2} - \frac{38}{3}e + 1$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{1}{3}e^{5} - \frac{14}{3}e^{4} + 5e^{3} + 16e^{2} - \frac{43}{3}e - 17$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}e^{7} - 4e^{6} - 5e^{5} + \frac{91}{3}e^{4} - 2e^{3} - \frac{188}{3}e^{2} + \frac{67}{3}e + \frac{94}{3}$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{2}{3}e^{6} - \frac{10}{3}e^{5} + 3e^{4} + 14e^{3} + 2e^{2} - \frac{64}{3}e - \frac{20}{3}$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $-\frac{4}{3}e^{7} + \frac{17}{3}e^{6} + \frac{20}{3}e^{5} - \frac{136}{3}e^{4} + \frac{19}{3}e^{3} + 94e^{2} - \frac{134}{3}e - \frac{80}{3}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}\frac{4}{3}e^{6} - \frac{11}{3}e^{5} - 11e^{4} + \frac{77}{3}e^{3} + \frac{85}{3}e^{2} - 40e - \frac{40}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $-1$ |