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: | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 36x^{10} + 490x^{8} - 3132x^{6} + 9413x^{4} - 11088x^{2} + 2304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 16 | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $\phantom{-}\frac{11}{1344}e^{11} - \frac{27}{112}e^{9} + \frac{1627}{672}e^{7} - \frac{1049}{112}e^{5} + \frac{15055}{1344}e^{3} - \frac{45}{14}e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $-1$ |
| 29 | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $-\frac{1}{56}e^{10} + \frac{4}{7}e^{8} - \frac{181}{28}e^{6} + \frac{214}{7}e^{4} - \frac{3013}{56}e^{2} + \frac{114}{7}$ |
| 31 | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $\phantom{-}\frac{1}{112}e^{11} - \frac{2}{7}e^{9} + \frac{181}{56}e^{7} - \frac{107}{7}e^{5} + \frac{3069}{112}e^{3} - \frac{163}{14}e$ |
| 41 | $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ | $\phantom{-}\frac{3}{224}e^{11} - \frac{3}{7}e^{9} + \frac{557}{112}e^{7} - \frac{178}{7}e^{5} + \frac{12371}{224}e^{3} - \frac{493}{14}e$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ | $\phantom{-}\frac{11}{1344}e^{11} - \frac{27}{112}e^{9} + \frac{1627}{672}e^{7} - \frac{1021}{112}e^{5} + \frac{9679}{1344}e^{3} + \frac{267}{28}e$ |
| 59 | $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ | $\phantom{-}\frac{1}{112}e^{11} - \frac{2}{7}e^{9} + \frac{181}{56}e^{7} - \frac{435}{28}e^{5} + \frac{3461}{112}e^{3} - \frac{529}{28}e$ |
| 61 | $[61, 61, w^{5} - 7w^{3} + 10w]$ | $-\frac{1}{56}e^{10} + \frac{4}{7}e^{8} - \frac{181}{28}e^{6} + \frac{421}{14}e^{4} - \frac{2649}{56}e^{2} + \frac{16}{7}$ |
| 61 | $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ | $-\frac{1}{84}e^{11} + \frac{19}{56}e^{9} - \frac{521}{168}e^{7} + \frac{481}{56}e^{5} + \frac{1079}{168}e^{3} - \frac{197}{7}e$ |
| 71 | $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ | $-\frac{1}{192}e^{11} + \frac{3}{16}e^{9} - \frac{245}{96}e^{7} + \frac{253}{16}e^{5} - \frac{7877}{192}e^{3} + \frac{121}{4}e$ |
| 71 | $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ | $\phantom{-}\frac{3}{112}e^{10} - \frac{6}{7}e^{8} + \frac{543}{56}e^{6} - \frac{635}{14}e^{4} + \frac{8535}{112}e^{2} - \frac{150}{7}$ |
| 71 | $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ | $\phantom{-}\frac{13}{1344}e^{11} - \frac{37}{112}e^{9} + \frac{2717}{672}e^{7} - \frac{2347}{112}e^{5} + \frac{54569}{1344}e^{3} - \frac{345}{28}e$ |
| 79 | $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ | $-\frac{1}{224}e^{11} + \frac{1}{7}e^{9} - \frac{167}{112}e^{7} + \frac{36}{7}e^{5} - \frac{17}{224}e^{3} - \frac{66}{7}e$ |
| 79 | $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ | $-\frac{11}{672}e^{11} + \frac{27}{56}e^{9} - \frac{1627}{336}e^{7} + \frac{1035}{56}e^{5} - \frac{12031}{672}e^{3} - \frac{331}{28}e$ |
| 79 | $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ | $-\frac{1}{4}e^{6} + \frac{9}{2}e^{4} - \frac{81}{4}e^{2} + 16$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ | $-\frac{23}{1344}e^{11} + \frac{59}{112}e^{9} - \frac{3799}{672}e^{7} + \frac{2789}{112}e^{5} - \frac{57259}{1344}e^{3} + \frac{829}{28}e$ |
| 89 | $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ | $\phantom{-}\frac{11}{1344}e^{11} - \frac{27}{112}e^{9} + \frac{1627}{672}e^{7} - \frac{1077}{112}e^{5} + \frac{19087}{1344}e^{3} - \frac{251}{28}e$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ | $\phantom{-}\frac{1}{56}e^{10} - \frac{4}{7}e^{8} + \frac{181}{28}e^{6} - \frac{207}{7}e^{4} + \frac{2397}{56}e^{2} + \frac{12}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $1$ |