Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, w^{3} - 5w]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 9x^{3} - 12x^{2} + 20x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{5}{4}e^{2} + 2e + 1$ |
11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{1}{4}e^{4} + \frac{9}{4}e^{2} + \frac{1}{2}e - 3$ |
13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $-\frac{1}{4}e^{4} + \frac{9}{4}e^{2} + \frac{1}{2}e - 1$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{7}{2}e^{2} - 3e + 7$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + e + 6$ |
19 | $[19, 19, w^{3} - 5w]$ | $-1$ |
19 | $[19, 19, -w + 3]$ | $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} + \frac{3}{2}e - 7$ |
23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{9}{4}e^{2} - 2e + 1$ |
23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{1}{4}e^{4} + 2e^{3} - \frac{1}{4}e^{2} - \frac{23}{2}e + 1$ |
25 | $[25, 5, w^{2} - 3]$ | $\phantom{-}e^{2} + e - 6$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{3}{2}e^{2} + 4e + 4$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e + 9$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{5}{2}e^{2} + \frac{19}{2}e - 3$ |
47 | $[47, 47, w^{3} - 6w + 1]$ | $-e^{3} - 2e^{2} + 6e + 10$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{13}{4}e^{2} - 3e + 5$ |
67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $\phantom{-}\frac{3}{4}e^{4} + \frac{1}{2}e^{3} - \frac{27}{4}e^{2} - 3e + 9$ |
67 | $[67, 67, w^{3} - 7w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} - e - 2$ |
73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $-\frac{5}{4}e^{4} - \frac{1}{2}e^{3} + \frac{45}{4}e^{2} - e - 17$ |
81 | $[81, 3, -3]$ | $-\frac{3}{4}e^{4} - e^{3} + \frac{27}{4}e^{2} + \frac{3}{2}e - 17$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, w^{3} - 5w]$ | $1$ |