Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^5 - x^4 - 5 x^3 + 2 x^2 + 3 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[47, 47, w^4 - 2 w^3 - 3 w^2 + 5 w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 + 5 x^5 - 3 x^4 - 31 x^3 + 2 x^2 + 43 x - 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^4 - 6 w^2 - 2 w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^4 + w^3 + 5 w^2 - w - 4]$ | $\phantom{-}\frac{4}{11} e^5 + 2 e^4 - \frac{1}{11} e^3 - \frac{119}{11} e^2 - \frac{57}{11} e + \frac{83}{11}$ |
| 11 | $[11, 11, -2 w^4 + w^3 + 10 w^2 + w - 3]$ | $-\frac{6}{11} e^5 - 3 e^4 - \frac{4}{11} e^3 + \frac{173}{11} e^2 + \frac{113}{11} e - \frac{174}{11}$ |
| 11 | $[11, 11, w^4 - 6 w^2 - 3 w + 3]$ | $\phantom{-}\frac{3}{11} e^5 + e^4 - \frac{20}{11} e^3 - \frac{59}{11} e^2 + \frac{48}{11} e + \frac{32}{11}$ |
| 17 | $[17, 17, w^2 - 2]$ | $\phantom{-}\frac{7}{11} e^5 + 4 e^4 + \frac{23}{11} e^3 - \frac{233}{11} e^2 - \frac{196}{11} e + \frac{247}{11}$ |
| 23 | $[23, 23, -w^3 + w^2 + 3 w]$ | $\phantom{-}\frac{1}{11} e^5 + e^4 + \frac{19}{11} e^3 - \frac{71}{11} e^2 - \frac{116}{11} e + \frac{84}{11}$ |
| 27 | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w - 1]$ | $-\frac{7}{11} e^5 - 3 e^4 + \frac{21}{11} e^3 + \frac{178}{11} e^2 + \frac{20}{11} e - \frac{148}{11}$ |
| 29 | $[29, 29, 2 w^4 - 2 w^3 - 9 w^2 + 2 w + 3]$ | $-\frac{3}{11} e^5 - 2 e^4 - \frac{13}{11} e^3 + \frac{136}{11} e^2 + \frac{84}{11} e - \frac{197}{11}$ |
| 32 | $[32, 2, -2]$ | $-\frac{12}{11} e^5 - 7 e^4 - \frac{41}{11} e^3 + \frac{412}{11} e^2 + \frac{336}{11} e - \frac{447}{11}$ |
| 47 | $[47, 47, w^4 - 2 w^3 - 3 w^2 + 5 w]$ | $-1$ |
| 47 | $[47, 47, w^3 - w^2 - 4 w - 1]$ | $\phantom{-}\frac{8}{11} e^5 + 4 e^4 - \frac{2}{11} e^3 - \frac{249}{11} e^2 - \frac{136}{11} e + \frac{254}{11}$ |
| 53 | $[53, 53, -w^4 + 7 w^2 - 3]$ | $-\frac{6}{11} e^5 - 3 e^4 + \frac{7}{11} e^3 + \frac{206}{11} e^2 + \frac{91}{11} e - \frac{229}{11}$ |
| 53 | $[53, 53, 2 w^4 - 2 w^3 - 9 w^2 + 2 w + 2]$ | $-\frac{1}{11} e^5 + \frac{14}{11} e^3 - \frac{17}{11} e^2 - \frac{60}{11} e + \frac{37}{11}$ |
| 53 | $[53, 53, 3 w^4 - 2 w^3 - 16 w^2 + 8]$ | $-\frac{1}{11} e^5 - e^4 - \frac{19}{11} e^3 + \frac{60}{11} e^2 + \frac{72}{11} e - \frac{95}{11}$ |
| 67 | $[67, 67, -w^4 + 6 w^2 + 4 w - 3]$ | $-\frac{12}{11} e^5 - 6 e^4 + \frac{3}{11} e^3 + \frac{357}{11} e^2 + \frac{127}{11} e - \frac{326}{11}$ |
| 73 | $[73, 73, 2 w^4 - 12 w^2 - 4 w + 5]$ | $\phantom{-}\frac{3}{11} e^5 + 2 e^4 + \frac{24}{11} e^3 - \frac{81}{11} e^2 - \frac{106}{11} e - \frac{23}{11}$ |
| 83 | $[83, 83, w^4 - 5 w^2 - 3 w + 3]$ | $\phantom{-}e^4 + 3 e^3 - 7 e^2 - 14 e + 14$ |
| 97 | $[97, 97, -w^4 + w^3 + 5 w^2 - 3 w - 3]$ | $\phantom{-}\frac{9}{11} e^5 + 5 e^4 + \frac{6}{11} e^3 - \frac{342}{11} e^2 - \frac{175}{11} e + \frac{338}{11}$ |
| 103 | $[103, 103, 2 w^3 - 3 w^2 - 7 w + 3]$ | $\phantom{-}\frac{1}{11} e^5 - \frac{14}{11} e^3 + \frac{6}{11} e^2 + \frac{16}{11} e - \frac{4}{11}$ |
| 109 | $[109, 109, -3 w^4 + 2 w^3 + 14 w^2 + w - 6]$ | $\phantom{-}\frac{12}{11} e^5 + 7 e^4 + \frac{52}{11} e^3 - \frac{346}{11} e^2 - \frac{336}{11} e + \frac{249}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47, 47, w^4 - 2 w^3 - 3 w^2 + 5 w]$ | $1$ |