Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 28x^{2} + 16x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ | $\phantom{-}0$ |
5 | $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ | $\phantom{-}\frac{1}{24}e^{3} + \frac{1}{3}e^{2} - \frac{1}{3}e + \frac{1}{3}$ |
5 | $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ | $\phantom{-}\frac{1}{24}e^{3} + \frac{1}{3}e^{2} - \frac{1}{3}e - \frac{11}{3}$ |
9 | $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ | $-2$ |
19 | $[19, 19, -w]$ | $\phantom{-}e$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ | $-\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{1}{3}e + \frac{4}{3}$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - \frac{23}{3}e - \frac{4}{3}$ |
19 | $[19, 19, w - 1]$ | $-\frac{1}{4}e^{3} - e^{2} + 7e - 4$ |
29 | $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ | $-\frac{7}{24}e^{3} - \frac{11}{6}e^{2} + \frac{10}{3}e + \frac{17}{3}$ |
29 | $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{2}e^{2} - 2e + 5$ |
29 | $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ | $\phantom{-}\frac{3}{8}e^{3} + \frac{3}{2}e^{2} - 10e + 3$ |
29 | $[29, 29, -w + 3]$ | $-\frac{13}{24}e^{3} - \frac{17}{6}e^{2} + \frac{34}{3}e - \frac{1}{3}$ |
49 | $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ | $\phantom{-}\frac{1}{4}e^{3} + e^{2} - 8e - 2$ |
49 | $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ | $-\frac{1}{4}e^{3} - e^{2} + 8e - 6$ |
71 | $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ | $-\frac{7}{12}e^{3} - \frac{8}{3}e^{2} + \frac{44}{3}e - \frac{2}{3}$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ | $\phantom{-}\frac{7}{12}e^{3} + \frac{8}{3}e^{2} - \frac{44}{3}e + \frac{14}{3}$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ | $\phantom{-}\frac{1}{12}e^{3} + \frac{2}{3}e^{2} + \frac{4}{3}e - \frac{10}{3}$ |
71 | $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ | $-\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{4}{3}e - \frac{2}{3}$ |
101 | $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ | $-\frac{11}{24}e^{3} - \frac{8}{3}e^{2} + \frac{23}{3}e - \frac{5}{3}$ |
101 | $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ | $\phantom{-}\frac{5}{24}e^{3} + \frac{2}{3}e^{2} - \frac{17}{3}e + \frac{35}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ | $-1$ |