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