Base field 4.4.9225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[36, 6, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{11}{4}]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 12x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $-1$ |
4 | $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ | $\phantom{-}e$ |
9 | $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ | $-1$ |
11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 7$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ | $\phantom{-}e + 1$ |
19 | $[19, 19, w]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 7$ |
19 | $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$ |
25 | $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$ |
29 | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}e + 3$ |
29 | $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ | $-e^{2} + e + 12$ |
41 | $[41, 41, -w^{3} + 7w + 3]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 6$ |
41 | $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ | $\phantom{-}e^{2} - 3e - 14$ |
41 | $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ | $\phantom{-}e^{2} - 7$ |
71 | $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ | $\phantom{-}\frac{5}{2}e^{2} - \frac{3}{2}e - 18$ |
71 | $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ | $-e^{2} + 17$ |
79 | $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ | $-e^{2} + e - 2$ |
79 | $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ | $\phantom{-}e^{2} + e - 4$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ | $-\frac{5}{2}e^{2} + \frac{1}{2}e + 19$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ | $\phantom{-}\frac{5}{2}e^{2} - \frac{3}{2}e - 20$ |
101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ | $-3e - 5$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $1$ |
$9$ | $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ | $1$ |