Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19,19,-w + 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 4x^{2} - 12x + 36\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}e$ |
9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} + e + 5$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}e - 3$ |
19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{6}e^{2} + \frac{5}{3}e - 1$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{1}{2}e^{2} + 9$ |
19 | $[19, 19, -w + 2]$ | $-1$ |
25 | $[25, 5, 2w^{2} - 2w - 13]$ | $-\frac{1}{3}e^{2} + \frac{1}{3}e + 1$ |
29 | $[29, 29, -w^{2} + 9]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - 5$ |
29 | $[29, 29, -w^{2} + 2w + 6]$ | $-\frac{1}{3}e^{2} - \frac{2}{3}e + 2$ |
29 | $[29, 29, w^{2} - 7]$ | $\phantom{-}4$ |
29 | $[29, 29, -w^{2} + 2w + 8]$ | $\phantom{-}e - 2$ |
31 | $[31, 31, -2w^{2} + w + 12]$ | $\phantom{-}2e - 2$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-\frac{1}{2}e^{2} + 7$ |
41 | $[41, 41, -w]$ | $-\frac{1}{3}e^{2} - \frac{2}{3}e + 6$ |
41 | $[41, 41, -w + 1]$ | $\phantom{-}\frac{1}{6}e^{2} + \frac{4}{3}e - 3$ |
49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}e - 14$ |
49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $-\frac{1}{3}e^{2} + \frac{4}{3}e + 2$ |
61 | $[61, 61, 2w^{2} - 3w - 14]$ | $-\frac{2}{3}e^{2} + \frac{5}{3}e$ |
61 | $[61, 61, 2w^{2} - w - 15]$ | $-\frac{1}{3}e^{2} + \frac{7}{3}e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,-w + 2]$ | $1$ |