Base field 6.6.1387029.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - x^{2} - 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37, 37, w^{3} - w^{2} - 4w + 2]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - 11x^{16} + 27x^{15} + 118x^{14} - 642x^{13} + 117x^{12} + 4264x^{11} - 5833x^{10} - 11153x^{9} + 27250x^{8} + 6873x^{7} - 52200x^{6} + 17038x^{5} + 41733x^{4} - 25278x^{3} - 9245x^{2} + 7057x - 331\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ | $...$ |
| 25 | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ | $...$ |
| 37 | $[37, 37, w^{3} - w^{2} - 4w + 2]$ | $-1$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $...$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ | $...$ |
| 49 | $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ | $...$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $...$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $...$ |
| 61 | $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ | $...$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ | $...$ |
| 61 | $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ | $...$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ | $...$ |
| 64 | $[64, 2, -2]$ | $...$ |
| 67 | $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ | $...$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ | $...$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ | $...$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $...$ |
| 81 | $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ | $...$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, w^{3} - w^{2} - 4w + 2]$ | $1$ |