Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[11, 11, w^{2} - 2w - 2]$ |
Dimension: | $16$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} - 24x^{14} + 2x^{13} + 231x^{12} - 35x^{11} - 1140x^{10} + 233x^{9} + 3059x^{8} - 739x^{7} - 4357x^{6} + 1145x^{5} + 2958x^{4} - 787x^{3} - 713x^{2} + 186x + 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $...$ |
7 | $[7, 7, w^{2} - 2w - 8]$ | $...$ |
7 | $[7, 7, -2w^{2} + 3w + 16]$ | $...$ |
7 | $[7, 7, -w^{2} + 2w + 6]$ | $...$ |
11 | $[11, 11, w^{2} - 2w - 2]$ | $\phantom{-}1$ |
19 | $[19, 19, -w + 2]$ | $...$ |
23 | $[23, 23, -w^{2} + 3w + 1]$ | $...$ |
25 | $[25, 5, w^{2} - w - 9]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, -w^{2} - w + 1]$ | $...$ |
29 | $[29, 29, w^{2} - 2w - 4]$ | $...$ |
29 | $[29, 29, -w^{2} + w + 11]$ | $...$ |
43 | $[43, 43, 2w^{2} - 3w - 18]$ | $...$ |
47 | $[47, 47, -2w + 7]$ | $...$ |
53 | $[53, 53, w^{2} - w - 3]$ | $...$ |
61 | $[61, 61, w^{2} + 2w + 2]$ | $...$ |
67 | $[67, 67, -2w^{2} + 5w + 8]$ | $...$ |
79 | $[79, 79, w^{2} - 3w - 9]$ | $...$ |
97 | $[97, 97, -w^{2} - 2w + 2]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, w^{2} - 2w - 2]$ | $-1$ |