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: | $[19,19,\frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ |
Dimension: | $8$ |
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:
\(x^{8} - 32x^{6} + 334x^{4} - 1143x^{2} + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ | $\phantom{-}\frac{4}{39}e^{6} - \frac{31}{13}e^{4} + \frac{532}{39}e^{2} - \frac{112}{39}$ |
5 | $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ | $-\frac{7}{351}e^{7} + \frac{10}{13}e^{5} - \frac{3310}{351}e^{3} + \frac{12754}{351}e$ |
9 | $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ | $-\frac{19}{351}e^{6} + \frac{16}{13}e^{4} - \frac{2215}{351}e^{2} - \frac{482}{351}$ |
19 | $[19, 19, -w]$ | $\phantom{-}\frac{61}{351}e^{6} - \frac{50}{13}e^{4} + \frac{6982}{351}e^{2} + \frac{2231}{351}$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ | $-1$ |
19 | $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ | $\phantom{-}\frac{61}{351}e^{6} - \frac{50}{13}e^{4} + \frac{6982}{351}e^{2} + \frac{2231}{351}$ |
19 | $[19, 19, w - 1]$ | $-\frac{44}{351}e^{6} + \frac{35}{13}e^{4} - \frac{4760}{351}e^{2} - \frac{211}{351}$ |
29 | $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ | $-\frac{8}{117}e^{7} + \frac{25}{13}e^{5} - \frac{1961}{117}e^{3} + \frac{5333}{117}e$ |
29 | $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ | $\phantom{-}\frac{23}{351}e^{7} - \frac{18}{13}e^{5} + \frac{1850}{351}e^{3} + \frac{5830}{351}e$ |
29 | $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ | $\phantom{-}\frac{4}{27}e^{7} - 4e^{5} + \frac{877}{27}e^{3} - \frac{2050}{27}e$ |
29 | $[29, 29, -w + 3]$ | $-\frac{31}{351}e^{7} + \frac{35}{13}e^{5} - \frac{9193}{351}e^{3} + \frac{28402}{351}e$ |
49 | $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ | $\phantom{-}\frac{110}{351}e^{6} - \frac{94}{13}e^{4} + \frac{14357}{351}e^{2} - \frac{2456}{351}$ |
49 | $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ | $-\frac{148}{351}e^{6} + \frac{126}{13}e^{4} - \frac{18787}{351}e^{2} + \frac{1141}{351}$ |
71 | $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ | $-\frac{7}{351}e^{7} - \frac{3}{13}e^{5} + \frac{4763}{351}e^{3} - \frac{31472}{351}e$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ | $\phantom{-}\frac{7}{351}e^{7} + \frac{3}{13}e^{5} - \frac{4412}{351}e^{3} + \frac{27260}{351}e$ |
71 | $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ | $-\frac{58}{351}e^{7} + \frac{55}{13}e^{5} - \frac{11029}{351}e^{3} + \frac{21085}{351}e$ |
71 | $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ | $\phantom{-}\frac{4}{39}e^{7} - \frac{31}{13}e^{5} + \frac{571}{39}e^{3} - \frac{580}{39}e$ |
101 | $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ | $-\frac{38}{351}e^{7} + \frac{45}{13}e^{5} - \frac{12854}{351}e^{3} + \frac{45719}{351}e$ |
101 | $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ | $\phantom{-}\frac{43}{351}e^{7} - \frac{41}{13}e^{5} + \frac{8800}{351}e^{3} - \frac{22186}{351}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,\frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ | $1$ |