Base field \(\Q(\zeta_{11})^+\)
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[131,131,w^{4} - w^{3} - 5w^{2} + w + 5]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 6x^{4} - 13x^{3} + 146x^{2} - 295x + 164\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{23}{2}e + 20$ |
23 | $[23, 23, -w^{4} + 3w^{2} + w - 2]$ | $-e^{4} + 3e^{3} + 22e^{2} - 81e + 55$ |
23 | $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ | $-e^{4} + 3e^{3} + 22e^{2} - 81e + 55$ |
23 | $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{19}{4}e^{3} - \frac{133}{4}e^{2} + \frac{499}{4}e - 81$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{3}{2}e^{4} - 5e^{3} - 33e^{2} + \frac{263}{2}e - 91$ |
32 | $[32, 2, 2]$ | $-\frac{1}{4}e^{4} + \frac{3}{4}e^{3} + \frac{25}{4}e^{2} - \frac{39}{2}e + 5$ |
43 | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{19}{2}e + 16$ |
43 | $[43, 43, -w^{4} + 2w^{2} + w + 1]$ | $-e^{4} + 3e^{3} + 22e^{2} - 79e + 51$ |
43 | $[43, 43, w^{3} + w^{2} - 4w - 2]$ | $-e^{4} + 3e^{3} + 22e^{2} - 79e + 51$ |
43 | $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ | $-\frac{1}{4}e^{4} + e^{3} + 6e^{2} - \frac{101}{4}e + 14$ |
43 | $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ | $-e^{4} + \frac{7}{2}e^{3} + \frac{43}{2}e^{2} - \frac{185}{2}e + 71$ |
67 | $[67, 67, 2w^{4} - 7w^{2} + 2]$ | $-e^{4} + 4e^{3} + 21e^{2} - 104e + 91$ |
67 | $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ | $\phantom{-}\frac{7}{2}e^{4} - \frac{23}{2}e^{3} - \frac{151}{2}e^{2} + 303e - 225$ |
67 | $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ | $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - 11e^{2} + \frac{105}{2}e - 40$ |
67 | $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ | $-\frac{5}{4}e^{4} + 4e^{3} + 28e^{2} - \frac{425}{4}e + 69$ |
67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{4}e^{3} - \frac{45}{4}e^{2} + \frac{183}{4}e - 30$ |
89 | $[89, 89, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{23}{2}e^{2} + 41e - 22$ |
89 | $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ | $\phantom{-}2e^{4} - \frac{13}{2}e^{3} - \frac{89}{2}e^{2} + \frac{339}{2}e - 101$ |
89 | $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ | $-2e^{4} + \frac{13}{2}e^{3} + \frac{87}{2}e^{2} - \frac{343}{2}e + 124$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$131$ | $[131,131,w^{4} - w^{3} - 5w^{2} + w + 5]$ | $-1$ |