Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 8, w]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 36x^{8} + 400x^{6} - 1648x^{4} + 2048x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}0$ |
2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $-\frac{1}{176}e^{8} + \frac{31}{176}e^{6} - \frac{16}{11}e^{4} + \frac{79}{22}e^{2} - \frac{13}{11}$ |
5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $\phantom{-}\frac{9}{704}e^{9} - \frac{39}{88}e^{7} + \frac{199}{44}e^{5} - \frac{669}{44}e^{3} + \frac{98}{11}e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{3}{704}e^{9} - \frac{13}{88}e^{7} + \frac{35}{22}e^{5} - \frac{311}{44}e^{3} + \frac{128}{11}e$ |
19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}\frac{3}{176}e^{9} - \frac{13}{22}e^{7} + \frac{269}{44}e^{5} - \frac{245}{11}e^{3} + \frac{226}{11}e$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{176}e^{8} - \frac{21}{88}e^{6} + \frac{141}{44}e^{4} - \frac{155}{11}e^{2} + \frac{112}{11}$ |
31 | $[31, 31, -w^{2} + w + 1]$ | $\phantom{-}\frac{7}{704}e^{9} - \frac{17}{44}e^{7} + \frac{211}{44}e^{5} - \frac{953}{44}e^{3} + \frac{273}{11}e$ |
47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{5}{704}e^{9} - \frac{9}{44}e^{7} + \frac{29}{22}e^{5} - \frac{27}{44}e^{3} - \frac{47}{11}e$ |
49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $-e$ |
53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $-\frac{1}{176}e^{8} + \frac{21}{88}e^{6} - \frac{141}{44}e^{4} + \frac{166}{11}e^{2} - \frac{134}{11}$ |
53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2$ |
61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $-\frac{1}{2}e^{3} + 7e$ |
61 | $[61, 61, 2w^{2} - 7]$ | $-\frac{7}{704}e^{9} + \frac{17}{44}e^{7} - \frac{211}{44}e^{5} + \frac{953}{44}e^{3} - \frac{240}{11}e$ |
71 | $[71, 71, w^{2} - 3w - 5]$ | $\phantom{-}\frac{3}{176}e^{8} - \frac{41}{88}e^{6} + \frac{115}{44}e^{4} - \frac{3}{11}e^{2} - \frac{16}{11}$ |
73 | $[73, 73, 2w - 3]$ | $\phantom{-}\frac{15}{704}e^{9} - \frac{65}{88}e^{7} + \frac{339}{44}e^{5} - \frac{1313}{44}e^{3} + \frac{398}{11}e$ |
73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $\phantom{-}\frac{5}{704}e^{9} - \frac{9}{44}e^{7} + \frac{29}{22}e^{5} - \frac{5}{44}e^{3} - \frac{124}{11}e$ |
79 | $[79, 79, 2w^{2} - 5]$ | $\phantom{-}\frac{1}{88}e^{8} - \frac{31}{88}e^{6} + \frac{117}{44}e^{4} - \frac{24}{11}e^{2} - \frac{40}{11}$ |
81 | $[81, 3, -3]$ | $-\frac{1}{44}e^{8} + \frac{31}{44}e^{6} - \frac{64}{11}e^{4} + \frac{158}{11}e^{2} - \frac{30}{11}$ |
101 | $[101, 101, 2w^{2} - 4w - 9]$ | $-\frac{3}{704}e^{9} + \frac{13}{88}e^{7} - \frac{35}{22}e^{5} + \frac{311}{44}e^{3} - \frac{128}{11}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{2} + 2]$ | $1$ |