Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[7, 7, -2w^{2} + 2w + 17]$ |
Dimension: | $21$ |
CM: | no |
Base change: | no |
Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} - 4x^{20} - 27x^{19} + 117x^{18} + 301x^{17} - 1440x^{16} - 1810x^{15} + 9739x^{14} + 6480x^{13} - 39572x^{12} - 14680x^{11} + 98995x^{10} + 22686x^{9} - 149796x^{8} - 25612x^{7} + 128722x^{6} + 18992x^{5} - 54768x^{4} - 6032x^{3} + 8456x^{2} - 64x - 96\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
2 | $[2, 2, w^{2} - 2w - 5]$ | $...$ |
5 | $[5, 5, w^{2} + 3w + 1]$ | $...$ |
7 | $[7, 7, -2w^{2} + 2w + 17]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{2} + w + 9]$ | $...$ |
13 | $[13, 13, 2w + 1]$ | $...$ |
25 | $[25, 5, -3w^{2} + 5w + 19]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, w^{2} + w - 1]$ | $...$ |
31 | $[31, 31, w^{2} - w - 1]$ | $...$ |
37 | $[37, 37, 2w^{2} + 6w + 3]$ | $...$ |
41 | $[41, 41, -6w^{2} - 14w - 3]$ | $...$ |
53 | $[53, 53, -4w^{2} + 6w + 27]$ | $...$ |
59 | $[59, 59, 2w^{2} - 4w - 11]$ | $...$ |
61 | $[61, 61, w^{2} - w - 3]$ | $...$ |
61 | $[61, 61, -2w^{2} + 2w + 13]$ | $...$ |
73 | $[73, 73, w^{2} + 3w + 3]$ | $...$ |
97 | $[97, 97, w^{2} + w - 15]$ | $...$ |
101 | $[101, 101, w^{2} + 3w - 1]$ | $...$ |
101 | $[101, 101, w^{2} - w - 11]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -2w^{2} + 2w + 17]$ | $-1$ |