Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ |
Dimension: | $21$ |
CM: | no |
Base change: | no |
Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} - 10x^{20} + 7x^{19} + 230x^{18} - 631x^{17} - 1779x^{16} + 8128x^{15} + 4228x^{14} - 47880x^{13} + 12519x^{12} + 154771x^{11} - 92571x^{10} - 294638x^{9} + 211665x^{8} + 336874x^{7} - 231988x^{6} - 223597x^{5} + 122072x^{4} + 75417x^{3} - 26063x^{2} - 8453x + 1681\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $...$ |
11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $...$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $...$ |
13 | $[13, 13, -w + 2]$ | $...$ |
17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $...$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $...$ |
19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $...$ |
23 | $[23, 23, w^{2} - 2w - 1]$ | $...$ |
27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-1$ |
29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $...$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $...$ |
41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $...$ |
53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $...$ |
59 | $[59, 59, w - 4]$ | $...$ |
67 | $[67, 67, 2w^{2} - 3w - 8]$ | $...$ |
73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $...$ |
89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $...$ |
97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $...$ |
97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$27$ | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $1$ |