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: | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 23x^{8} + 176x^{6} - 528x^{4} + 559x^{2} - 121\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{5}{88}e^{9} - \frac{13}{11}e^{7} + \frac{15}{2}e^{5} - 15e^{3} + \frac{375}{88}e$ |
| 16 | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $-\frac{5}{176}e^{9} + \frac{13}{22}e^{7} - \frac{7}{2}e^{5} + \frac{9}{2}e^{3} + \frac{637}{176}e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $-\frac{1}{16}e^{8} + \frac{5}{4}e^{6} - \frac{29}{4}e^{4} + \frac{45}{4}e^{2} + \frac{13}{16}$ |
| 29 | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $-1$ |
| 31 | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $\phantom{-}\frac{3}{44}e^{9} - \frac{69}{44}e^{7} + \frac{47}{4}e^{5} - \frac{127}{4}e^{3} + \frac{481}{22}e$ |
| 41 | $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ | $\phantom{-}\frac{1}{88}e^{9} - \frac{3}{22}e^{7} - \frac{1}{2}e^{5} + \frac{17}{2}e^{3} - \frac{1157}{88}e$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ | $\phantom{-}\frac{7}{44}e^{9} - \frac{75}{22}e^{7} + 23e^{5} - \frac{109}{2}e^{3} + \frac{1537}{44}e$ |
| 59 | $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ | $-\frac{9}{176}e^{9} + \frac{49}{44}e^{7} - \frac{31}{4}e^{5} + \frac{79}{4}e^{3} - \frac{3227}{176}e$ |
| 61 | $[61, 61, w^{5} - 7w^{3} + 10w]$ | $-\frac{1}{2}e^{4} + 5e^{2} - \frac{5}{2}$ |
| 61 | $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ | $\phantom{-}\frac{3}{176}e^{9} - \frac{9}{44}e^{7} - \frac{1}{4}e^{5} + \frac{25}{4}e^{3} - \frac{1535}{176}e$ |
| 71 | $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ | $-\frac{1}{22}e^{9} + \frac{23}{22}e^{7} - 8e^{5} + \frac{47}{2}e^{3} - \frac{427}{22}e$ |
| 71 | $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ | $-\frac{1}{2}e^{4} + 5e^{2} - \frac{9}{2}$ |
| 71 | $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ | $-\frac{1}{88}e^{9} + \frac{3}{22}e^{7} + \frac{1}{2}e^{5} - \frac{17}{2}e^{3} + \frac{1685}{88}e$ |
| 79 | $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ | $\phantom{-}\frac{1}{22}e^{9} - \frac{23}{22}e^{7} + 8e^{5} - \frac{49}{2}e^{3} + \frac{625}{22}e$ |
| 79 | $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ | $-\frac{3}{88}e^{9} + \frac{10}{11}e^{7} - 8e^{5} + 26e^{3} - \frac{2205}{88}e$ |
| 79 | $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{17}{4}e^{4} + \frac{69}{4}e^{2} - \frac{5}{4}$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ | $-e^{3} + 7e$ |
| 89 | $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ | $\phantom{-}\frac{1}{16}e^{9} - \frac{5}{4}e^{7} + \frac{29}{4}e^{5} - \frac{45}{4}e^{3} - \frac{45}{16}e$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{5}{2}e^{6} + 15e^{4} - \frac{59}{2}e^{2} + \frac{151}{8}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $1$ |