Base field 6.6.722000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 7x^{3} + 4x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49,7,w^{2} - 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 9x^{3} - 7x^{2} + 9x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} - w^{2} - 6w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, 3w^{5} - 2w^{4} - 19w^{3} + 14w^{2} + 18w - 9]$ | $\phantom{-}\frac{7}{11}e^{4} + \frac{12}{11}e^{3} - \frac{68}{11}e^{2} - \frac{39}{11}e + \frac{38}{11}$ |
| 29 | $[29, 29, -w^{2} - w + 2]$ | $-\frac{5}{11}e^{4} - \frac{18}{11}e^{3} + \frac{36}{11}e^{2} + \frac{86}{11}e - \frac{46}{11}$ |
| 29 | $[29, 29, 2w^{5} - w^{4} - 13w^{3} + 7w^{2} + 14w - 3]$ | $-e^{2} - 2e + 2$ |
| 29 | $[29, 29, -2w^{5} + w^{4} + 13w^{3} - 8w^{2} - 15w + 6]$ | $-\frac{13}{11}e^{4} - \frac{16}{11}e^{3} + \frac{120}{11}e^{2} - \frac{14}{11}e - \frac{102}{11}$ |
| 49 | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ | $-\frac{19}{11}e^{4} - \frac{31}{11}e^{3} + \frac{172}{11}e^{2} + \frac{76}{11}e - \frac{122}{11}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ | $-\frac{5}{11}e^{4} - \frac{7}{11}e^{3} + \frac{47}{11}e^{2} - \frac{24}{11}e - \frac{46}{11}$ |
| 49 | $[49, 7, w^{2} - 3]$ | $\phantom{-}1$ |
| 59 | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ | $-\frac{6}{11}e^{4} - \frac{26}{11}e^{3} + \frac{41}{11}e^{2} + \frac{156}{11}e - \frac{64}{11}$ |
| 59 | $[59, 59, 2w^{5} - 12w^{3} + 3w^{2} + 12w - 3]$ | $\phantom{-}\frac{12}{11}e^{4} + \frac{30}{11}e^{3} - \frac{82}{11}e^{2} - \frac{103}{11}e + \frac{18}{11}$ |
| 59 | $[59, 59, -2w^{5} + w^{4} + 12w^{3} - 8w^{2} - 11w + 3]$ | $\phantom{-}\frac{5}{11}e^{4} - \frac{4}{11}e^{3} - \frac{80}{11}e^{2} + \frac{46}{11}e + \frac{112}{11}$ |
| 61 | $[61, 61, -4w^{5} + 2w^{4} + 24w^{3} - 16w^{2} - 19w + 8]$ | $\phantom{-}\frac{12}{11}e^{4} + \frac{19}{11}e^{3} - \frac{115}{11}e^{2} - \frac{26}{11}e + \frac{18}{11}$ |
| 61 | $[61, 61, 5w^{5} - 3w^{4} - 31w^{3} + 22w^{2} + 27w - 13]$ | $-\frac{24}{11}e^{4} - \frac{49}{11}e^{3} + \frac{197}{11}e^{2} + \frac{162}{11}e - \frac{102}{11}$ |
| 61 | $[61, 61, 3w^{5} - w^{4} - 18w^{3} + 9w^{2} + 16w - 4]$ | $-\frac{2}{11}e^{4} - \frac{5}{11}e^{3} + \frac{21}{11}e^{2} - \frac{3}{11}e - \frac{124}{11}$ |
| 71 | $[71, 71, 2w^{5} - 12w^{3} + 2w^{2} + 11w - 1]$ | $\phantom{-}\frac{12}{11}e^{4} + \frac{30}{11}e^{3} - \frac{93}{11}e^{2} - \frac{136}{11}e + \frac{84}{11}$ |
| 71 | $[71, 71, 3w^{5} - 2w^{4} - 18w^{3} + 15w^{2} + 13w - 9]$ | $\phantom{-}\frac{7}{11}e^{4} + \frac{23}{11}e^{3} - \frac{35}{11}e^{2} - \frac{61}{11}e - \frac{50}{11}$ |
| 71 | $[71, 71, -w^{5} + w^{4} + 6w^{3} - 7w^{2} - 6w + 5]$ | $-\frac{8}{11}e^{4} + \frac{2}{11}e^{3} + \frac{95}{11}e^{2} - \frac{100}{11}e - \frac{100}{11}$ |
| 79 | $[79, 79, -w^{5} + 7w^{3} - w^{2} - 10w]$ | $\phantom{-}\frac{9}{11}e^{4} + \frac{28}{11}e^{3} - \frac{67}{11}e^{2} - \frac{135}{11}e + \frac{30}{11}$ |
| 79 | $[79, 79, 4w^{5} - 2w^{4} - 25w^{3} + 15w^{2} + 23w - 9]$ | $-e^{3} - 2e^{2} + 4e + 4$ |
| 79 | $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ | $-\frac{8}{11}e^{4} - \frac{9}{11}e^{3} + \frac{73}{11}e^{2} + \frac{10}{11}e - \frac{12}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49,7,w^{2} - 3]$ | $-1$ |