Base field 4.4.7600.1
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[29, 29, -w^{3} + 4w + 2]$ |
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:
\(x^{8} - 19x^{6} + 115x^{4} - 233x^{2} + 128\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
9 | $[9, 3, -w^{2} - w + 4]$ | $-\frac{1}{8}e^{7} + \frac{13}{8}e^{5} - \frac{47}{8}e^{3} + \frac{59}{8}e$ |
9 | $[9, 3, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{31}{4}e$ |
11 | $[11, 11, w + 1]$ | $-\frac{1}{8}e^{7} + \frac{17}{8}e^{5} - \frac{83}{8}e^{3} + \frac{99}{8}e$ |
11 | $[11, 11, w - 1]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e$ |
19 | $[19, 19, -w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$ |
19 | $[19, 19, -w^{2} - w + 6]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{17}{4}e^{2}$ |
19 | $[19, 19, -w^{2} + w + 6]$ | $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{75}{4}e^{2} - 18$ |
25 | $[25, 5, 2w^{2} - 9]$ | $-\frac{1}{4}e^{6} + 3e^{4} - \frac{31}{4}e^{2} + 2$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $-1$ |
29 | $[29, 29, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{9}{2}e^{4} + \frac{93}{4}e^{2} - 26$ |
41 | $[41, 41, 2w^{2} - w - 7]$ | $\phantom{-}e^{5} - 10e^{3} + 17e$ |
41 | $[41, 41, w^{3} - w^{2} - 6w + 4]$ | $\phantom{-}e^{5} - 10e^{3} + 17e$ |
61 | $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{93}{4}e^{3} - 28e$ |
61 | $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{5}{2}e^{3} + \frac{13}{4}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{9}{2}e$ |
61 | $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ | $-\frac{1}{8}e^{7} + \frac{19}{8}e^{5} - \frac{107}{8}e^{3} + \frac{145}{8}e$ |
89 | $[89, 89, -w^{3} + w^{2} + 6w - 9]$ | $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{75}{4}e^{2} - 22$ |
89 | $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ | $-\frac{1}{4}e^{6} + e^{4} + \frac{33}{4}e^{2} - 6$ |
109 | $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ | $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{17}{4}e^{3} + e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, -w^{3} + 4w + 2]$ | $1$ |