Base field \(\Q(\sqrt{317}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 79\); 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: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{21} + 9x^{20} - 8x^{19} - 283x^{18} - 445x^{17} + 3218x^{16} + 8974x^{15} - 15079x^{14} - 68507x^{13} + 13051x^{12} + 256519x^{11} + 130296x^{10} - 472710x^{9} - 459967x^{8} + 345103x^{7} + 540247x^{6} + 10433x^{5} - 180595x^{4} - 39500x^{3} + 11587x^{2} + 2252x - 247\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w - 8]$ | $...$ |
| 7 | $[7, 7, -w + 9]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w - 10]$ | $...$ |
| 11 | $[11, 11, -w - 9]$ | $...$ |
| 23 | $[23, 23, -w - 7]$ | $...$ |
| 23 | $[23, 23, -w + 8]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, -w - 10]$ | $...$ |
| 31 | $[31, 31, w - 11]$ | $...$ |
| 37 | $[37, 37, -w - 6]$ | $...$ |
| 37 | $[37, 37, w - 7]$ | $...$ |
| 43 | $[43, 43, 4w + 33]$ | $...$ |
| 43 | $[43, 43, 4w - 37]$ | $...$ |
| 53 | $[53, 53, -w - 11]$ | $...$ |
| 53 | $[53, 53, w - 12]$ | $...$ |
| 59 | $[59, 59, -w - 4]$ | $...$ |
| 59 | $[59, 59, w - 5]$ | $...$ |
| 61 | $[61, 61, 2w - 17]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,w - 9]$ | $-1$ |