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: | $[9, 3, 3]$ |
Dimension: | $26$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{26} - 27x^{25} + 274x^{24} - 954x^{23} - 4101x^{22} + 47461x^{21} - 108708x^{20} - 434150x^{19} + 2816627x^{18} - 2521695x^{17} - 20213273x^{16} + 61179183x^{15} + 12853398x^{14} - 337066055x^{13} + 458045142x^{12} + 524838157x^{11} - 1915039329x^{10} + 994509134x^{9} + 2277494750x^{8} - 3296518617x^{7} + 256317343x^{6} + 2242786830x^{5} - 1396222786x^{4} - 140389982x^{3} + 382720392x^{2} - 115421299x + 10230765\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w - 8]$ | $...$ |
7 | $[7, 7, -w + 9]$ | $...$ |
9 | $[9, 3, 3]$ | $-1$ |
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 |
---|---|---|
$9$ | $[9, 3, 3]$ | $1$ |