Base field 4.4.14656.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 18x^{6} + 107x^{4} - 228x^{2} + 92\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{3}{16}e^{6} + \frac{5}{2}e^{4} - \frac{145}{16}e^{2} + \frac{49}{8}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{8}e^{6} - 2e^{4} + \frac{67}{8}e^{2} - \frac{27}{4}$ |
| 11 | $[11, 11, w^{2} - 3]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{1}{2}e^{5} - \frac{21}{16}e^{3} + \frac{77}{8}e$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 1]$ | $-\frac{1}{16}e^{7} + \frac{1}{2}e^{5} + \frac{21}{16}e^{3} - \frac{93}{8}e$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - w + 5]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{1}{2}e^{5} + \frac{11}{16}e^{3} - \frac{19}{8}e$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + w - 1]$ | $-\frac{5}{8}e^{6} + 9e^{4} - \frac{271}{8}e^{2} + \frac{79}{4}$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{6} + 6e^{4} - \frac{35}{2}e^{2} + 3$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + \frac{71}{4}e^{3} - \frac{37}{2}e$ |
| 47 | $[47, 47, w^{2} - 2w - 5]$ | $-\frac{1}{8}e^{7} + e^{5} + \frac{13}{8}e^{3} - \frac{53}{4}e$ |
| 47 | $[47, 47, -2w^{3} + 6w^{2} + w - 5]$ | $-\frac{7}{8}e^{7} + 12e^{5} - \frac{341}{8}e^{3} + \frac{101}{4}e$ |
| 61 | $[61, 61, -2w^{3} + 5w^{2} + 4w - 7]$ | $-\frac{5}{8}e^{6} + 9e^{4} - \frac{263}{8}e^{2} + \frac{55}{4}$ |
| 67 | $[67, 67, -2w^{2} + 2w + 9]$ | $-\frac{1}{8}e^{7} + 2e^{5} - \frac{83}{8}e^{3} + \frac{63}{4}e$ |
| 67 | $[67, 67, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{7}{16}e^{7} - \frac{11}{2}e^{5} + \frac{237}{16}e^{3} + \frac{43}{8}e$ |
| 71 | $[71, 71, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{5}{8}e^{7} - 8e^{5} + \frac{191}{8}e^{3} + \frac{1}{4}e$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{5}{16}e^{7} - \frac{9}{2}e^{5} + \frac{295}{16}e^{3} - \frac{159}{8}e$ |
| 89 | $[89, 89, -w - 3]$ | $-\frac{5}{8}e^{6} + 8e^{4} - \frac{207}{8}e^{2} + \frac{15}{4}$ |
| 89 | $[89, 89, -w^{2} - 2w + 1]$ | $\phantom{-}e^{6} - 13e^{4} + 43e^{2} - 24$ |
| 97 | $[97, 97, w^{3} - w^{2} - 6w + 1]$ | $\phantom{-}e^{6} - 13e^{4} + 45e^{2} - 34$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 3]$ | $-1$ |