Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, -w^{3} + w^{2} + 6w]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 13x^{4} + 47x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 5w - 2]$ | $-e^{3} + 6e$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-e$ |
13 | $[13, 13, -w + 2]$ | $-\frac{1}{4}e^{5} + \frac{9}{4}e^{3} - \frac{19}{4}e$ |
16 | $[16, 2, 2]$ | $-e^{2} + 1$ |
17 | $[17, 17, w^{3} - w^{2} - 5w]$ | $\phantom{-}e^{2} - 6$ |
19 | $[19, 19, -w^{3} + w^{2} + 6w]$ | $\phantom{-}1$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-\frac{1}{4}e^{5} + \frac{9}{4}e^{3} - \frac{15}{4}e$ |
29 | $[29, 29, w^{3} - 5w]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - \frac{19}{2}e$ |
31 | $[31, 31, w^{3} - 6w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + \frac{7}{2}e$ |
31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{5}{4}e^{3} - \frac{9}{4}e$ |
37 | $[37, 37, -w - 3]$ | $-e^{4} + 8e^{2} - 14$ |
37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{1}{4}e^{5} + \frac{9}{4}e^{3} - \frac{11}{4}e$ |
37 | $[37, 37, w^{3} - 7w - 4]$ | $\phantom{-}3e^{4} - 21e^{2} + 18$ |
37 | $[37, 37, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + \frac{15}{2}e$ |
43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}e^{5} - 8e^{3} + 12e$ |
43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $-e^{4} + 7e^{2} - 12$ |
47 | $[47, 47, -w^{3} + w^{2} + 5w - 4]$ | $-2e^{4} + 12e^{2} - 4$ |
53 | $[53, 53, w^{3} - 6w]$ | $\phantom{-}\frac{5}{4}e^{5} - \frac{29}{4}e^{3} - \frac{9}{4}e$ |
61 | $[61, 61, w^{3} - w^{2} - 7w - 2]$ | $-e^{4} + 4e^{2} + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{3} + w^{2} + 6w]$ | $-1$ |