Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + 2x^{19} - 35x^{18} - 68x^{17} + 488x^{16} + 951x^{15} - 3407x^{14} - 7046x^{13} + 12062x^{12} + 29423x^{11} - 17362x^{10} - 67019x^{9} - 7852x^{8} + 72126x^{7} + 43502x^{6} - 21904x^{5} - 27514x^{4} - 3979x^{3} + 4290x^{2} + 1929x + 241\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $...$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -3w - 17]$ | $...$ |
| 11 | $[11, 11, 3w - 20]$ | $...$ |
| 13 | $[13, 13, 2w - 13]$ | $...$ |
| 13 | $[13, 13, 2w + 11]$ | $...$ |
| 17 | $[17, 17, w + 7]$ | $...$ |
| 17 | $[17, 17, -w + 8]$ | $...$ |
| 19 | $[19, 19, -w - 4]$ | $...$ |
| 19 | $[19, 19, -w + 5]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, -6w - 35]$ | $...$ |
| 31 | $[31, 31, -6w + 41]$ | $...$ |
| 37 | $[37, 37, -w - 1]$ | $...$ |
| 37 | $[37, 37, w - 2]$ | $...$ |
| 47 | $[47, 47, 3w + 16]$ | $...$ |
| 47 | $[47, 47, -3w + 19]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 67 | $[67, 67, 3w - 22]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |