Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 11 x^2 + 12 x + 31\); 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:
| \(x^8 - 14 x^6 + 42 x^4 - 22 x^2 + 1\) |
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 | $[11, 11, \frac{1}{2} w^3 - 4 w - \frac{7}{2}]$ | $-\frac{1}{4} e^6 + \frac{13}{4} e^4 - \frac{29}{4} e^2 + \frac{9}{4}$ |
| 11 | $[11, 11, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{5}{2} w - 7]$ | $-1$ |
| 19 | $[19, 19, -w^2 + 2 w + 4]$ | $\phantom{-}e^7 - 14 e^5 + 41 e^3 - 14 e$ |
| 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 | $[31, 31, w]$ | $-\frac{1}{2} e^6 + 7 e^4 - \frac{39}{2} e^2 + 3$ |
| 31 | $[31, 31, w + 3]$ | $-\frac{1}{4} e^6 + \frac{13}{4} e^4 - \frac{25}{4} e^2 - \frac{11}{4}$ |
| 31 | $[31, 31, -w + 4]$ | $\phantom{-}e^6 - \frac{27}{2} e^4 + 36 e^2 - \frac{13}{2}$ |
| 31 | $[31, 31, w - 1]$ | $-\frac{1}{2} e^4 + 4 e^2 + \frac{3}{2}$ |
| 41 | $[41, 41, -w^2 + 2]$ | $-e^6 + 14 e^4 - 41 e^2 + 14$ |
| 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 | $[59, 59, -\frac{1}{2} w^3 + 2 w^2 + 2 w - \frac{17}{2}]$ | $\phantom{-}\frac{3}{2} e^7 - \frac{43}{2} e^5 + \frac{139}{2} e^3 - \frac{101}{2} e$ |
| 79 | $[79, 79, -w^2 + 8]$ | $-3 e^7 + \frac{83}{2} e^5 - 119 e^3 + \frac{97}{2} e$ |
| 79 | $[79, 79, w^2 - 2 w - 7]$ | $-3 e^7 + 42 e^5 - 126 e^3 + 63 e$ |
| 81 | $[81, 3, -3]$ | $-e^6 + 14 e^4 - 41 e^2 + 10$ |
| 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 | $[101, 101, w^3 - \frac{5}{2} w^2 - \frac{11}{2} w + \frac{17}{2}]$ | $-\frac{1}{2} e^6 + 7 e^4 - \frac{37}{2} e^2 + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{5}{2} w - 7]$ | $1$ |