Base field \(\Q(\sqrt{389}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 97\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, -w - 9]$ |
| Dimension: | $21$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $71$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{21} + 10x^{20} + 3x^{19} - 265x^{18} - 651x^{17} + 2417x^{16} + 9830x^{15} - 7049x^{14} - 63856x^{13} - 19811x^{12} + 209862x^{11} + 178456x^{10} - 349300x^{9} - 441644x^{8} + 259733x^{7} + 488325x^{6} - 39421x^{5} - 243053x^{4} - 37989x^{3} + 41742x^{2} + 11664x + 729\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -3w - 28]$ | $...$ |
| 5 | $[5, 5, -3w + 31]$ | $...$ |
| 7 | $[7, 7, -w - 9]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w + 10]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, -2w - 19]$ | $...$ |
| 11 | $[11, 11, 2w - 21]$ | $...$ |
| 13 | $[13, 13, w - 11]$ | $...$ |
| 13 | $[13, 13, -w - 10]$ | $...$ |
| 17 | $[17, 17, -8w - 75]$ | $...$ |
| 17 | $[17, 17, -8w + 83]$ | $...$ |
| 19 | $[19, 19, -5w + 52]$ | $...$ |
| 19 | $[19, 19, 5w + 47]$ | $...$ |
| 41 | $[41, 41, -w - 7]$ | $...$ |
| 41 | $[41, 41, w - 8]$ | $...$ |
| 59 | $[59, 59, -w - 12]$ | $...$ |
| 59 | $[59, 59, w - 13]$ | $...$ |
| 67 | $[67, 67, -w - 5]$ | $...$ |
| 67 | $[67, 67, w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w - 9]$ | $-1$ |