Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11,11,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 14x^{6} + 42x^{4} - 22x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $-\frac{5}{4}e^{7} + \frac{69}{4}e^{5} - \frac{197}{4}e^{3} + \frac{77}{4}e$ |
4 | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 3]$ | $-\frac{1}{4}e^{7} + \frac{13}{4}e^{5} - \frac{29}{4}e^{3} - \frac{7}{4}e$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ | $-\frac{1}{4}e^{6} + \frac{13}{4}e^{4} - \frac{29}{4}e^{2} + \frac{9}{4}$ |
11 | $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $-1$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}e^{7} - 14e^{5} + 41e^{3} - 14e$ |
19 | $[19, 19, -w^{2} + 5]$ | $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - \frac{29}{2}e^{3} - \frac{9}{2}e$ |
31 | $[31, 31, w]$ | $-\frac{1}{2}e^{6} + 7e^{4} - \frac{39}{2}e^{2} + 3$ |
31 | $[31, 31, w + 3]$ | $-\frac{1}{4}e^{6} + \frac{13}{4}e^{4} - \frac{25}{4}e^{2} - \frac{11}{4}$ |
31 | $[31, 31, -w + 4]$ | $\phantom{-}e^{6} - \frac{27}{2}e^{4} + 36e^{2} - \frac{13}{2}$ |
31 | $[31, 31, w - 1]$ | $-\frac{1}{2}e^{4} + 4e^{2} + \frac{3}{2}$ |
41 | $[41, 41, -w^{2} + 2]$ | $-e^{6} + 14e^{4} - 41e^{2} + 14$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ | $-\frac{3}{4}e^{6} + \frac{41}{4}e^{4} - \frac{111}{4}e^{2} + \frac{33}{4}$ |
59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ | $-\frac{1}{4}e^{7} + \frac{13}{4}e^{5} - \frac{29}{4}e^{3} + \frac{9}{4}e$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ | $\phantom{-}\frac{3}{2}e^{7} - \frac{43}{2}e^{5} + \frac{139}{2}e^{3} - \frac{101}{2}e$ |
79 | $[79, 79, -w^{2} + 8]$ | $-3e^{7} + \frac{83}{2}e^{5} - 119e^{3} + \frac{97}{2}e$ |
79 | $[79, 79, w^{2} - 2w - 7]$ | $-3e^{7} + 42e^{5} - 126e^{3} + 63e$ |
81 | $[81, 3, -3]$ | $-e^{6} + 14e^{4} - 41e^{2} + 10$ |
101 | $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ | $-\frac{1}{2}e^{6} + \frac{15}{2}e^{4} - \frac{51}{2}e^{2} + \frac{33}{2}$ |
101 | $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ | $-\frac{1}{2}e^{6} + 7e^{4} - \frac{37}{2}e^{2} + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $1$ |