Base field 6.6.1312625.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 7x^{3} + 12x^{2} - 12x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 6x^{5} + x^{4} + 38x^{3} - 25x^{2} - 57x + 37\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - 2e^{3} + \frac{24}{7}e^{2} + \frac{36}{7}e - \frac{39}{7}$ |
| 16 | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $-1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - 2e^{3} + \frac{17}{7}e^{2} + \frac{57}{7}e - \frac{32}{7}$ |
| 29 | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $-\frac{3}{7}e^{5} + \frac{13}{7}e^{4} - \frac{37}{7}e^{2} + \frac{32}{7}e - \frac{2}{7}$ |
| 31 | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $-\frac{2}{7}e^{5} + \frac{4}{7}e^{4} + 4e^{3} - \frac{48}{7}e^{2} - \frac{72}{7}e + \frac{113}{7}$ |
| 41 | $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{9}{7}e^{4} + e^{3} + \frac{59}{7}e^{2} - \frac{27}{7}e - \frac{67}{7}$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ | $-\frac{2}{7}e^{5} + \frac{11}{7}e^{4} - 2e^{3} - \frac{20}{7}e^{2} + \frac{75}{7}e - \frac{20}{7}$ |
| 59 | $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ | $-\frac{5}{7}e^{5} + \frac{31}{7}e^{4} - 2e^{3} - \frac{141}{7}e^{2} + \frac{65}{7}e + \frac{90}{7}$ |
| 61 | $[61, 61, w^{5} - 7w^{3} + 10w]$ | $-e^{4} + 3e^{3} + 5e^{2} - 8e - 11$ |
| 61 | $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ | $-\frac{5}{7}e^{5} + \frac{17}{7}e^{4} + 4e^{3} - \frac{92}{7}e^{2} - \frac{33}{7}e + \frac{132}{7}$ |
| 71 | $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ | $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + 4e^{3} - \frac{73}{7}e^{2} - \frac{71}{7}e + \frac{158}{7}$ |
| 71 | $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ | $\phantom{-}\frac{3}{7}e^{5} - \frac{13}{7}e^{4} + \frac{37}{7}e^{2} - \frac{25}{7}e - \frac{33}{7}$ |
| 71 | $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ | $\phantom{-}\frac{8}{7}e^{5} - \frac{37}{7}e^{4} - e^{3} + \frac{150}{7}e^{2} - \frac{34}{7}e - \frac{81}{7}$ |
| 79 | $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - e^{3} + \frac{10}{7}e^{2} - \frac{6}{7}e + \frac{3}{7}$ |
| 79 | $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ | $\phantom{-}\frac{3}{7}e^{5} - \frac{6}{7}e^{4} - 5e^{3} + \frac{30}{7}e^{2} + \frac{108}{7}e + \frac{9}{7}$ |
| 79 | $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ | $-\frac{5}{7}e^{5} + \frac{24}{7}e^{4} + 3e^{3} - \frac{155}{7}e^{2} - \frac{19}{7}e + \frac{167}{7}$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ | $-\frac{3}{7}e^{5} - \frac{1}{7}e^{4} + 6e^{3} + \frac{26}{7}e^{2} - \frac{87}{7}e - \frac{37}{7}$ |
| 89 | $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ | $\phantom{-}\frac{4}{7}e^{5} - \frac{15}{7}e^{4} - 3e^{3} + \frac{82}{7}e^{2} + \frac{11}{7}e - \frac{37}{7}$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ | $-e^{4} + 3e^{3} + 3e^{2} - 5e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $1$ |