Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[27, 27, -w^{2} + w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 45x^{4} + 306x^{2} - 567\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{14}{3}e^{2} + 16$ |
11 | $[11, 11, -w - 2]$ | $-\frac{7}{9}e^{4} + 32e^{2} - 114$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{5}{27}e^{5} - \frac{23}{3}e^{3} + \frac{86}{3}e$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{4}{27}e^{5} - 6e^{3} + \frac{55}{3}e$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{4}{9}e^{4} - \frac{55}{3}e^{2} + 64$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-\frac{2}{3}e^{4} + \frac{82}{3}e^{2} - 99$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{4}{9}e^{4} - 18e^{2} + 60$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $-\frac{5}{27}e^{5} + \frac{23}{3}e^{3} - \frac{89}{3}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}e^{4} - 41e^{2} + 141$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-\frac{2}{9}e^{5} + 9e^{3} - 29e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{4}{9}e^{5} + \frac{55}{3}e^{3} - 67e$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{14}{27}e^{5} + \frac{64}{3}e^{3} - \frac{233}{3}e$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{11}{27}e^{5} + \frac{50}{3}e^{3} - \frac{167}{3}e$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $\phantom{-}\frac{16}{27}e^{5} - \frac{73}{3}e^{3} + \frac{256}{3}e$ |
83 | $[83, 83, -2w + 3]$ | $\phantom{-}\frac{5}{9}e^{4} - 23e^{2} + 84$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $-\frac{1}{3}e^{4} + \frac{40}{3}e^{2} - 48$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $-\frac{23}{27}e^{5} + 35e^{3} - \frac{368}{3}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |