Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 48x^{6} + 720x^{4} - 3456x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $\phantom{-}\frac{1}{128}e^{7} - \frac{21}{64}e^{5} + \frac{63}{16}e^{3} - \frac{109}{8}e$ |
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{64}e^{6} - \frac{9}{16}e^{4} + \frac{37}{8}e^{2} - \frac{5}{2}$ |
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{64}e^{7} + \frac{21}{32}e^{5} - \frac{63}{8}e^{3} + \frac{105}{4}e$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{1}{64}e^{7} - \frac{51}{64}e^{5} + \frac{51}{4}e^{3} - \frac{511}{8}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}\frac{1}{128}e^{7} - \frac{9}{64}e^{5} - \frac{45}{16}e^{3} + \frac{319}{8}e$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}\frac{3}{64}e^{6} - \frac{55}{32}e^{4} + \frac{113}{8}e^{2} - \frac{19}{4}$ |
| 31 | $[31, 31, -w^{3} + 7w + 5]$ | $-\frac{1}{64}e^{6} + \frac{19}{32}e^{4} - \frac{39}{8}e^{2} - \frac{25}{4}$ |
| 41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $-\frac{1}{128}e^{7} + \frac{3}{64}e^{5} + \frac{97}{16}e^{3} - \frac{525}{8}e$ |
| 41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $\phantom{-}\frac{17}{64}e^{5} - \frac{75}{8}e^{3} + \frac{589}{8}e$ |
| 67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{27}{8}e^{4} + \frac{105}{4}e^{2} + 8$ |
| 67 | $[67, 67, -w^{2} + 4w + 2]$ | $-\frac{3}{32}e^{6} + \frac{27}{8}e^{4} - \frac{105}{4}e^{2} - 10$ |
| 83 | $[83, 83, 2w^{2} - 5w - 2]$ | $-\frac{1}{128}e^{7} + \frac{11}{64}e^{5} + \frac{25}{16}e^{3} - \frac{221}{8}e$ |
| 83 | $[83, 83, -w^{3} + 8w + 6]$ | $\phantom{-}\frac{1}{64}e^{7} - \frac{53}{64}e^{5} + \frac{29}{2}e^{3} - \frac{681}{8}e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $-\frac{1}{32}e^{7} + \frac{95}{64}e^{5} - \frac{175}{8}e^{3} + \frac{811}{8}e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{3}{128}e^{7} - \frac{67}{64}e^{5} + \frac{233}{16}e^{3} - \frac{539}{8}e$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $\phantom{-}\frac{1}{64}e^{6} - \frac{17}{32}e^{4} + \frac{23}{8}e^{2} + \frac{67}{4}$ |
| 97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $-\frac{7}{64}e^{6} + \frac{125}{32}e^{4} - \frac{245}{8}e^{2} + \frac{1}{4}$ |
| 97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{27}{8}e^{4} + \frac{103}{4}e^{2} + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $-1$ |