Base field 4.4.12725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19,19,w^{2} - 6]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 5x^{3} - 14x^{2} - 68x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, -w - 1]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{3}{8}e^{2} - \frac{3}{2}e - \frac{7}{2}$ |
11 | $[11, 11, w^{2} - 5]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $-\frac{3}{16}e^{3} - \frac{9}{16}e^{2} + \frac{11}{4}e + \frac{17}{4}$ |
11 | $[11, 11, w - 2]$ | $\phantom{-}\frac{1}{4}e^{2} + \frac{1}{4}e - \frac{11}{2}$ |
16 | $[16, 2, 2]$ | $-\frac{1}{16}e^{3} + \frac{1}{16}e^{2} + \frac{1}{2}e - \frac{15}{4}$ |
19 | $[19, 19, w^{2} - 2w - 5]$ | $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{13}{4}e + \frac{7}{2}$ |
19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}1$ |
25 | $[25, 5, -2w^{2} + 2w + 11]$ | $\phantom{-}\frac{1}{16}e^{3} - \frac{1}{16}e^{2} - \frac{3}{2}e + \frac{3}{4}$ |
29 | $[29, 29, w]$ | $\phantom{-}\frac{1}{16}e^{3} - \frac{5}{16}e^{2} - \frac{7}{4}e - \frac{3}{4}$ |
29 | $[29, 29, 2w^{2} - w - 10]$ | $-e - 3$ |
29 | $[29, 29, -2w^{2} + 3w + 9]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{8}e^{2} - \frac{11}{4}e - 1$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{1}{4}e^{2} + \frac{5}{4}e - \frac{5}{2}$ |
31 | $[31, 31, w^{3} - 6w - 6]$ | $\phantom{-}2$ |
31 | $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ | $-\frac{1}{8}e^{3} + \frac{1}{8}e^{2} + 4e + \frac{1}{2}$ |
41 | $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{4}e^{2} - 5e + 4$ |
41 | $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ | $-\frac{1}{16}e^{3} + \frac{9}{16}e^{2} - \frac{43}{4}$ |
59 | $[59, 59, w^{3} - w^{2} - 5w - 2]$ | $-\frac{3}{16}e^{3} - \frac{17}{16}e^{2} + \frac{5}{4}e + \frac{29}{4}$ |
59 | $[59, 59, 2w^{2} - w - 13]$ | $\phantom{-}\frac{9}{16}e^{3} + \frac{27}{16}e^{2} - \frac{33}{4}e - \frac{51}{4}$ |
61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{16}e^{3} - \frac{9}{16}e^{2} - e + \frac{27}{4}$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{7}{16}e^{3} + \frac{5}{16}e^{2} - \frac{31}{4}e + \frac{15}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,w^{2} - 6]$ | $-1$ |