Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[11, 11, w^{2} - w - 1]$ |
Dimension: | $27$ |
CM: | no |
Base change: | no |
Newspace dimension: | $63$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{27} + 2x^{26} - 37x^{25} - 72x^{24} + 597x^{23} + 1131x^{22} - 5511x^{21} - 10172x^{20} + 32110x^{19} + 57766x^{18} - 123023x^{17} - 215462x^{16} + 313897x^{15} + 532452x^{14} - 531304x^{13} - 860574x^{12} + 588906x^{11} + 881679x^{10} - 419651x^{9} - 544806x^{8} + 183250x^{7} + 186546x^{6} - 42244x^{5} - 30334x^{4} + 2986x^{3} + 1751x^{2} + 137x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $...$ |
3 | $[3, 3, w^{2} - w - 9]$ | $...$ |
7 | $[7, 7, w^{2} - w - 7]$ | $...$ |
11 | $[11, 11, w^{2} - w - 1]$ | $-1$ |
13 | $[13, 13, -2w - 1]$ | $...$ |
17 | $[17, 17, -2w^{2} + 6w + 5]$ | $...$ |
31 | $[31, 31, -2w^{2} + 2w + 19]$ | $...$ |
37 | $[37, 37, 2w^{2} - 13]$ | $...$ |
41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
43 | $[43, 43, 2w^{2} - 2w - 17]$ | $...$ |
43 | $[43, 43, -2w + 7]$ | $...$ |
43 | $[43, 43, 12w^{2} - 8w - 101]$ | $...$ |
49 | $[49, 7, w^{2} + w - 1]$ | $...$ |
59 | $[59, 59, -w^{2} + w + 11]$ | $...$ |
61 | $[61, 61, -w^{2} - w - 1]$ | $...$ |
79 | $[79, 79, -2w^{2} + 4w + 7]$ | $...$ |
83 | $[83, 83, 2w - 1]$ | $...$ |
89 | $[89, 89, 5w^{2} - 3w - 43]$ | $...$ |
103 | $[103, 103, -2w + 5]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, w^{2} - w - 1]$ | $1$ |