Base field 6.6.1922000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 8x^{4} - x^{3} + 12x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[16, 2, -3w^{5} + 4w^{4} + 23w^{3} - 6w^{2} - 35w - 6]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 6x^{5} - 9x^{4} + 70x^{3} + 33x^{2} - 144x - 101\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $-\frac{1}{7}e^{5} + \frac{13}{14}e^{4} + \frac{4}{7}e^{3} - \frac{65}{7}e^{2} + \frac{17}{7}e + \frac{187}{14}$ |
| 11 | $[11, 11, -w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{13}{14}e^{4} - \frac{4}{7}e^{3} + \frac{65}{7}e^{2} - \frac{24}{7}e - \frac{145}{14}$ |
| 31 | $[31, 31, -4w^{5} + 6w^{4} + 28w^{3} - 8w^{2} - 39w - 11]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -4w^{5} + 5w^{4} + 31w^{3} - 4w^{2} - 49w - 16]$ | $\phantom{-}\frac{1}{14}e^{5} - \frac{3}{14}e^{4} - \frac{9}{7}e^{3} + \frac{15}{7}e^{2} + \frac{67}{14}e + \frac{1}{14}$ |
| 41 | $[41, 41, w^{4} - 3w^{3} - 3w^{2} + 8w + 1]$ | $-\frac{1}{7}e^{5} + \frac{13}{14}e^{4} + \frac{4}{7}e^{3} - \frac{72}{7}e^{2} + \frac{45}{7}e + \frac{257}{14}$ |
| 41 | $[41, 41, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{14}e^{5} - \frac{5}{7}e^{4} + \frac{5}{7}e^{3} + \frac{57}{7}e^{2} - \frac{157}{14}e - \frac{108}{7}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{4} - \frac{3}{2}e^{3} + \frac{75}{2}e^{2} - 15e - 51$ |
| 59 | $[59, 59, 4w^{5} - 5w^{4} - 31w^{3} + 4w^{2} + 49w + 14]$ | $-\frac{3}{14}e^{5} + \frac{23}{14}e^{4} - \frac{9}{14}e^{3} - \frac{209}{14}e^{2} + \frac{120}{7}e + \frac{156}{7}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 3w^{2} - 8w - 3]$ | $-\frac{2}{7}e^{5} + \frac{13}{7}e^{4} + \frac{9}{14}e^{3} - \frac{253}{14}e^{2} + \frac{159}{14}e + \frac{465}{14}$ |
| 71 | $[71, 71, 5w^{5} - 7w^{4} - 37w^{3} + 9w^{2} + 55w + 16]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{13}{2}e + \frac{7}{2}$ |
| 71 | $[71, 71, -w^{5} + 11w^{3} + 4w^{2} - 19w - 7]$ | $\phantom{-}\frac{3}{14}e^{5} - \frac{23}{14}e^{4} - \frac{5}{14}e^{3} + \frac{265}{14}e^{2} - \frac{57}{7}e - \frac{233}{7}$ |
| 71 | $[71, 71, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $-\frac{3}{14}e^{5} + \frac{23}{14}e^{4} - \frac{9}{14}e^{3} - \frac{209}{14}e^{2} + \frac{106}{7}e + \frac{135}{7}$ |
| 79 | $[79, 79, 3w^{5} - 6w^{4} - 17w^{3} + 11w^{2} + 21w + 7]$ | $\phantom{-}\frac{1}{14}e^{5} - \frac{5}{7}e^{4} + \frac{17}{14}e^{3} + \frac{93}{14}e^{2} - \frac{103}{7}e - \frac{153}{14}$ |
| 79 | $[79, 79, -5w^{5} + 8w^{4} + 35w^{3} - 14w^{2} - 52w - 11]$ | $-\frac{1}{14}e^{5} + \frac{5}{7}e^{4} - \frac{3}{14}e^{3} - \frac{121}{14}e^{2} + \frac{19}{7}e + \frac{251}{14}$ |
| 79 | $[79, 79, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{3}{2}e + \frac{25}{2}$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 14w^{3} - 3w^{2} - 21w - 9]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{13}{14}e^{4} - \frac{15}{14}e^{3} + \frac{165}{14}e^{2} + \frac{1}{14}e - \frac{160}{7}$ |
| 101 | $[101, 101, -2w^{5} + 2w^{4} + 17w^{3} - 29w - 9]$ | $-\frac{5}{14}e^{5} + \frac{18}{7}e^{4} - \frac{1}{14}e^{3} - \frac{353}{14}e^{2} + \frac{144}{7}e + \frac{527}{14}$ |
| 101 | $[101, 101, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 9w + 1]$ | $\phantom{-}\frac{5}{14}e^{5} - \frac{18}{7}e^{4} - \frac{13}{14}e^{3} + \frac{381}{14}e^{2} - \frac{67}{7}e - \frac{541}{14}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ | $1$ |