Base field 6.6.966125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[55, 55, -w^{3} + 5w + 1]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + 2x^{6} - 68x^{5} - 232x^{4} + 608x^{3} + 1984x^{2} - 1664x - 2560\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $\phantom{-}e$ |
25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{3}{32}e^{5} - \frac{27}{16}e^{4} + \frac{9}{8}e^{3} + \frac{61}{4}e^{2} - 8e - 18$ |
29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $\phantom{-}\frac{5}{64}e^{6} - \frac{1}{4}e^{5} - \frac{65}{16}e^{4} + \frac{25}{8}e^{3} + \frac{135}{4}e^{2} - 20e - 38$ |
31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{3}{16}e^{5} - \frac{13}{4}e^{4} + \frac{7}{4}e^{3} + \frac{51}{2}e^{2} - 12e - 24$ |
31 | $[31, 31, -w^{2} + 2]$ | $-\frac{3}{64}e^{6} + \frac{5}{32}e^{5} + \frac{39}{16}e^{4} - \frac{19}{8}e^{3} - \frac{41}{2}e^{2} + 19e + 20$ |
59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $-\frac{1}{64}e^{6} + \frac{1}{32}e^{5} + \frac{7}{8}e^{4} + \frac{1}{4}e^{3} - \frac{15}{2}e^{2} + e + 16$ |
59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{5}{32}e^{5} - \frac{27}{8}e^{4} + \frac{1}{2}e^{3} + \frac{107}{4}e^{2} - 9e - 28$ |
59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{8}e^{5} - \frac{25}{16}e^{4} + \frac{19}{8}e^{3} + \frac{29}{2}e^{2} - 11e - 24$ |
61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{9}{32}e^{5} - \frac{39}{8}e^{4} + \frac{21}{8}e^{3} + \frac{77}{2}e^{2} - 18e - 42$ |
64 | $[64, 2, 2]$ | $\phantom{-}\frac{3}{64}e^{6} - \frac{1}{8}e^{5} - \frac{41}{16}e^{4} + \frac{3}{4}e^{3} + 23e^{2} - 4e - 31$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $\phantom{-}\frac{1}{64}e^{6} - \frac{1}{16}e^{5} - \frac{3}{4}e^{4} + \frac{5}{4}e^{3} + \frac{21}{4}e^{2} - 11e$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $-\frac{3}{64}e^{6} + \frac{5}{32}e^{5} + \frac{5}{2}e^{4} - \frac{5}{2}e^{3} - \frac{47}{2}e^{2} + 16e + 32$ |
71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $-\frac{1}{16}e^{6} + \frac{5}{32}e^{5} + \frac{27}{8}e^{4} - \frac{3}{8}e^{3} - \frac{55}{2}e^{2} + 6e + 32$ |
71 | $[71, 71, w^{3} - 5w]$ | $-\frac{3}{32}e^{6} + \frac{9}{32}e^{5} + \frac{79}{16}e^{4} - \frac{23}{8}e^{3} - \frac{163}{4}e^{2} + 20e + 44$ |
79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{5}{64}e^{6} - \frac{1}{4}e^{5} - \frac{33}{8}e^{4} + \frac{13}{4}e^{3} + \frac{149}{4}e^{2} - 19e - 56$ |
89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{64}e^{6} - \frac{15}{16}e^{4} - 2e^{3} + 7e^{2} + 13e - 10$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $-\frac{1}{64}e^{6} + \frac{3}{32}e^{5} + \frac{3}{4}e^{4} - \frac{23}{8}e^{3} - \frac{39}{4}e^{2} + 13e + 22$ |
101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $-\frac{1}{64}e^{6} + \frac{1}{32}e^{5} + \frac{7}{8}e^{4} + \frac{1}{4}e^{3} - \frac{15}{2}e^{2} + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w - 1]$ | $-1$ |
$11$ | $[11, 11, w^{3} - 3w]$ | $-1$ |