Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} - 5x^{21} - 62x^{20} + 331x^{19} + 1521x^{18} - 9005x^{17} - 18358x^{16} + 129854x^{15} + 104802x^{14} - 1066331x^{13} - 132102x^{12} + 4977672x^{11} - 1259911x^{10} - 12521610x^{9} + 4941574x^{8} + 15759398x^{7} - 4656246x^{6} - 10544550x^{5} + 1108926x^{4} + 3543584x^{3} + 276186x^{2} - 455778x - 97146\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $...$ |
| 11 | $[11, 11, w - 1]$ | $...$ |
| 25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $...$ |
| 29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $...$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $...$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $-1$ |
| 59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $...$ |
| 59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $...$ |
| 61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $...$ |
| 61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $...$ |
| 64 | $[64, 2, 2]$ | $...$ |
| 71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $...$ |
| 71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $...$ |
| 79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $...$ |
| 81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $...$ |
| 89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $...$ |
| 89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $...$ |
| 89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $...$ |
| 89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $1$ |