Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[34, 34, -w^{5} + w^{4} + 4w^{3} - 3w^{2} - 2w + 2]$ |
Dimension: | $4$ |
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:
\(x^{4} + 12x^{3} + 42x^{2} + 25x - 51\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $-1$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $\phantom{-}1$ |
23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{2}{3}e^{3} - \frac{10}{3}e^{2} + \frac{4}{3}e + 5$ |
31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $\phantom{-}1$ |
32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $-\frac{5}{3}e^{3} - \frac{37}{3}e^{2} - \frac{44}{3}e + 19$ |
43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{29}{3}e^{2} + \frac{37}{3}e - 10$ |
47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $-\frac{2}{3}e^{3} - \frac{16}{3}e^{2} - \frac{26}{3}e + 1$ |
49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $-\frac{2}{3}e^{3} - \frac{13}{3}e^{2} - \frac{11}{3}e$ |
53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} + \frac{7}{3}e + 10$ |
59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{29}{3}e^{2} + \frac{22}{3}e - 26$ |
71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $\phantom{-}\frac{8}{3}e^{3} + \frac{55}{3}e^{2} + \frac{50}{3}e - 34$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{7}{3}e^{3} + \frac{50}{3}e^{2} + \frac{52}{3}e - 32$ |
83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{35}{3}e - 8$ |
83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $-\frac{8}{3}e^{3} - \frac{55}{3}e^{2} - \frac{53}{3}e + 27$ |
89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $\phantom{-}\frac{7}{3}e^{3} + \frac{50}{3}e^{2} + \frac{52}{3}e - 27$ |
89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $-e^{3} - 8e^{2} - 11e + 8$ |
89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $-\frac{2}{3}e^{3} - \frac{19}{3}e^{2} - \frac{41}{3}e$ |
89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $-\frac{4}{3}e^{3} - \frac{32}{3}e^{2} - \frac{49}{3}e + 18$ |
101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $-3e^{3} - 22e^{2} - 29e + 21$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w]$ | $1$ |
$17$ | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $-1$ |