Base field 6.6.703493.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 6x^{5} - 19x^{4} - 116x^{3} + 90x^{2} + 428x - 321\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ | $-e - 2$ |
| 13 | $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ | $\phantom{-}e$ |
| 13 | $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ | $\phantom{-}\frac{7}{243}e^{5} + \frac{50}{243}e^{4} - \frac{10}{27}e^{3} - \frac{902}{243}e^{2} + \frac{53}{243}e + \frac{688}{81}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-\frac{7}{243}e^{5} - \frac{20}{243}e^{4} + \frac{70}{81}e^{3} + \frac{278}{243}e^{2} - \frac{1541}{243}e - \frac{118}{81}$ |
| 41 | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $-\frac{11}{243}e^{5} - \frac{82}{243}e^{4} + \frac{31}{81}e^{3} + \frac{1336}{243}e^{2} + \frac{545}{243}e - \frac{1100}{81}$ |
| 41 | $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ | $\phantom{-}\frac{11}{243}e^{5} + \frac{28}{243}e^{4} - \frac{103}{81}e^{3} - \frac{310}{243}e^{2} + \frac{1939}{243}e - \frac{250}{81}$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $-\frac{11}{243}e^{5} - \frac{88}{243}e^{4} + \frac{23}{81}e^{3} + \frac{1558}{243}e^{2} + \frac{1523}{243}e - \frac{1538}{81}$ |
| 41 | $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ | $\phantom{-}\frac{11}{243}e^{5} + \frac{22}{243}e^{4} - \frac{37}{27}e^{3} - \frac{88}{243}e^{2} + \frac{1945}{243}e - \frac{1012}{81}$ |
| 43 | $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ | $-\frac{8}{243}e^{5} - \frac{46}{243}e^{4} + \frac{26}{81}e^{3} + \frac{445}{243}e^{2} + \frac{206}{243}e + \frac{409}{81}$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ | $\phantom{-}\frac{8}{243}e^{5} + \frac{34}{243}e^{4} - \frac{14}{27}e^{3} - \frac{487}{243}e^{2} - \frac{194}{243}e + \frac{497}{81}$ |
| 49 | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $\phantom{-}1$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1}{9}e^{4} + \frac{4}{9}e^{3} - \frac{19}{9}e^{2} - \frac{46}{9}e + \frac{4}{3}$ |
| 71 | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $\phantom{-}\frac{8}{243}e^{5} + \frac{19}{243}e^{4} - \frac{62}{81}e^{3} + \frac{68}{243}e^{2} + \frac{550}{243}e - \frac{1084}{81}$ |
| 71 | $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ | $-\frac{8}{243}e^{5} - \frac{61}{243}e^{4} + \frac{2}{27}e^{3} + \frac{1000}{243}e^{2} + \frac{1922}{243}e - \frac{848}{81}$ |
| 83 | $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ | $-\frac{8}{243}e^{5} - \frac{16}{243}e^{4} + \frac{22}{27}e^{3} + \frac{64}{243}e^{2} - \frac{1039}{243}e - \frac{236}{81}$ |
| 83 | $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ | $\phantom{-}\frac{8}{243}e^{5} + \frac{64}{243}e^{4} - \frac{2}{81}e^{3} - \frac{868}{243}e^{2} - \frac{953}{243}e + \frac{14}{81}$ |
| 97 | $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ | $-\frac{4}{243}e^{5} - \frac{44}{243}e^{4} - \frac{5}{27}e^{3} + \frac{878}{243}e^{2} + \frac{1825}{243}e - \frac{1288}{81}$ |
| 97 | $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ | $\phantom{-}\frac{4}{243}e^{5} - \frac{4}{243}e^{4} - \frac{49}{81}e^{3} + \frac{412}{243}e^{2} + \frac{1139}{243}e - \frac{1406}{81}$ |
| 113 | $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ | $-\frac{2}{9}e^{4} - \frac{8}{9}e^{3} + \frac{38}{9}e^{2} + \frac{92}{9}e - \frac{32}{3}$ |
| 113 | $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ | $\phantom{-}\frac{14}{243}e^{5} + \frac{124}{243}e^{4} - \frac{28}{81}e^{3} - \frac{2449}{243}e^{2} - \frac{1862}{243}e + \frac{2156}{81}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $-1$ |