Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[51, 51, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - 3w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 12x^{6} + 30x^{5} - 115x^{4} - 607x^{3} - 841x^{2} - 279x + 113\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $-\frac{7651}{25513}e^{6} - \frac{78129}{25513}e^{5} - \frac{90885}{25513}e^{4} + \frac{1032306}{25513}e^{3} + \frac{2792322}{25513}e^{2} + \frac{1596439}{25513}e - \frac{380647}{25513}$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $\phantom{-}\frac{2452}{25513}e^{6} + \frac{24532}{25513}e^{5} + \frac{24075}{25513}e^{4} - \frac{337587}{25513}e^{3} - \frac{831282}{25513}e^{2} - \frac{337419}{25513}e + \frac{169168}{25513}$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $-\frac{3960}{25513}e^{6} - \frac{39661}{25513}e^{5} - \frac{39464}{25513}e^{4} + \frac{536091}{25513}e^{3} + \frac{1329958}{25513}e^{2} + \frac{662802}{25513}e - \frac{213608}{25513}$ |
| 37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}\frac{10851}{25513}e^{6} + \frac{110436}{25513}e^{5} + \frac{126383}{25513}e^{4} - \frac{1460099}{25513}e^{3} - \frac{3916773}{25513}e^{2} - \frac{2173012}{25513}e + \frac{592431}{25513}$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $-\frac{12374}{25513}e^{6} - \frac{131417}{25513}e^{5} - \frac{189855}{25513}e^{4} + \frac{1681218}{25513}e^{3} + \frac{5160557}{25513}e^{2} + \frac{3308624}{25513}e - \frac{789985}{25513}$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $\phantom{-}\frac{392}{25513}e^{6} + \frac{3256}{25513}e^{5} - \frac{5474}{25513}e^{4} - \frac{72241}{25513}e^{3} - \frac{2335}{25513}e^{2} + \frac{301158}{25513}e + \frac{87685}{25513}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{8092}{25513}e^{6} + \frac{81792}{25513}e^{5} + \frac{91105}{25513}e^{4} - \frac{1084875}{25513}e^{3} - \frac{2900190}{25513}e^{2} - \frac{1608440}{25513}e + \frac{565399}{25513}$ |
| 71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $\phantom{-}\frac{14876}{25513}e^{6} + \frac{158447}{25513}e^{5} + \frac{229633}{25513}e^{4} - \frac{2034658}{25513}e^{3} - \frac{6247397}{25513}e^{2} - \frac{3940080}{25513}e + \frac{1112351}{25513}$ |
| 71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $-\frac{4451}{25513}e^{6} - \frac{45822}{25513}e^{5} - \frac{55387}{25513}e^{4} + \frac{604513}{25513}e^{3} + \frac{1667871}{25513}e^{2} + \frac{917814}{25513}e - \frac{449506}{25513}$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $\phantom{-}\frac{2870}{25513}e^{6} + \frac{31128}{25513}e^{5} + \frac{49218}{25513}e^{4} - \frac{389497}{25513}e^{3} - \frac{1264499}{25513}e^{2} - \frac{942304}{25513}e - \frac{69651}{25513}$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $\phantom{-}\frac{19058}{25513}e^{6} + \frac{203076}{25513}e^{5} + \frac{296977}{25513}e^{4} - \frac{2599295}{25513}e^{3} - \frac{8047674}{25513}e^{2} - \frac{5103216}{25513}e + \frac{1438749}{25513}$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $-\frac{15168}{25513}e^{6} - \frac{156707}{25513}e^{5} - \frac{192753}{25513}e^{4} + \frac{2075193}{25513}e^{3} + \frac{5764129}{25513}e^{2} + \frac{3025335}{25513}e - \frac{1327361}{25513}$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $\phantom{-}\frac{23517}{25513}e^{6} + \frac{240113}{25513}e^{5} + \frac{279358}{25513}e^{4} - \frac{3181852}{25513}e^{3} - \frac{8619575}{25513}e^{2} - \frac{4694456}{25513}e + \frac{1520887}{25513}$ |
| 89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $-\frac{73}{25513}e^{6} + \frac{435}{25513}e^{5} + \frac{9220}{25513}e^{4} + \frac{16512}{25513}e^{3} - \frac{95304}{25513}e^{2} - \frac{375386}{25513}e - \frac{347152}{25513}$ |
| 89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $-\frac{3799}{25513}e^{6} - \frac{34679}{25513}e^{5} - \frac{9821}{25513}e^{4} + \frac{505965}{25513}e^{3} + \frac{851997}{25513}e^{2} + \frac{118598}{25513}e - \frac{208119}{25513}$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $\phantom{-}\frac{6239}{25513}e^{6} + \frac{59632}{25513}e^{5} + \frac{41353}{25513}e^{4} - \frac{825460}{25513}e^{3} - \frac{1770941}{25513}e^{2} - \frac{710994}{25513}e + \frac{35384}{25513}$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $\phantom{-}\frac{1607}{25513}e^{6} + \frac{18034}{25513}e^{5} + \frac{36786}{25513}e^{4} - \frac{194685}{25513}e^{3} - \frac{834254}{25513}e^{2} - \frac{881553}{25513}e - \frac{139016}{25513}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $1$ |
| $17$ | $[17, 17, -w^{2} + 2w + 1]$ | $-1$ |