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: | $[20, 10, \frac{2}{19}w^{3} - \frac{3}{19}w^{2} + \frac{1}{19}w - 1]$ |
Dimension: | $4$ |
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:
\(x^{4} - 50x^{2} + 56x + 184\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ | $\phantom{-}1$ |
5 | $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ | $-\frac{1}{172}e^{3} - \frac{7}{86}e^{2} + \frac{13}{86}e + \frac{77}{43}$ |
9 | $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ | $\phantom{-}\frac{1}{172}e^{3} + \frac{7}{86}e^{2} - \frac{13}{86}e - \frac{120}{43}$ |
19 | $[19, 19, -w]$ | $\phantom{-}e$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ | $-\frac{1}{172}e^{3} - \frac{7}{86}e^{2} - \frac{73}{86}e + \frac{77}{43}$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ | $\phantom{-}\frac{2}{43}e^{3} + \frac{13}{86}e^{2} - \frac{52}{43}e - \frac{57}{43}$ |
19 | $[19, 19, w - 1]$ | $-\frac{3}{86}e^{3} + \frac{1}{86}e^{2} + \frac{39}{43}e - \frac{54}{43}$ |
29 | $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ | $-\frac{7}{172}e^{3} - \frac{3}{43}e^{2} + \frac{91}{86}e + \frac{195}{43}$ |
29 | $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ | $\phantom{-}\frac{7}{172}e^{3} + \frac{3}{43}e^{2} - \frac{91}{86}e + \frac{192}{43}$ |
29 | $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ | $-\frac{1}{43}e^{3} + \frac{15}{86}e^{2} + \frac{69}{43}e - \frac{122}{43}$ |
29 | $[29, 29, -w + 3]$ | $\phantom{-}\frac{9}{172}e^{3} + \frac{10}{43}e^{2} - \frac{203}{86}e - \frac{48}{43}$ |
49 | $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ | $-\frac{21}{172}e^{3} - \frac{9}{43}e^{2} + \frac{359}{86}e + \frac{198}{43}$ |
49 | $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ | $\phantom{-}\frac{5}{43}e^{3} + \frac{11}{86}e^{2} - \frac{173}{43}e + \frac{266}{43}$ |
71 | $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ | $-\frac{13}{172}e^{3} + \frac{19}{43}e^{2} + \frac{341}{86}e - \frac{461}{43}$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ | $\phantom{-}\frac{27}{172}e^{3} + \frac{30}{43}e^{2} - \frac{523}{86}e - \frac{316}{43}$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ | $\phantom{-}\frac{11}{172}e^{3} - \frac{9}{86}e^{2} - \frac{229}{86}e + \frac{486}{43}$ |
71 | $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ | $-\frac{4}{43}e^{3} - \frac{13}{43}e^{2} + \frac{147}{43}e + \frac{415}{43}$ |
101 | $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ | $\phantom{-}\frac{2}{43}e^{3} + \frac{28}{43}e^{2} - \frac{95}{43}e - \frac{616}{43}$ |
101 | $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ | $\phantom{-}\frac{7}{43}e^{3} - \frac{19}{86}e^{2} - \frac{354}{43}e + \frac{338}{43}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ | $-1$ |
$5$ | $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ | $-1$ |