Properties

 Label 4.4.14400.1-19.3-b Base field $$\Q(\sqrt{5}, \sqrt{6})$$ Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$ Dimension $8$ CM no Base change no

Related objects

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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: $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$ 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:

 $$x^{8} - 18x^{6} + 95x^{4} - 168x^{2} + 56$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $-\frac{3}{26}e^{6} + \frac{22}{13}e^{4} - \frac{147}{26}e^{2} + \frac{59}{13}$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $-\frac{1}{52}e^{7} + \frac{3}{26}e^{5} + \frac{81}{52}e^{3} - \frac{79}{13}e$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $\phantom{-}e$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $-\frac{3}{13}e^{6} + \frac{44}{13}e^{4} - \frac{147}{13}e^{2} + \frac{92}{13}$
19 $[19, 19, -w]$ $-\frac{5}{26}e^{6} + \frac{41}{13}e^{4} - \frac{323}{26}e^{2} + \frac{146}{13}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $-\frac{2}{13}e^{6} + \frac{25}{13}e^{4} - \frac{46}{13}e^{2} - \frac{8}{13}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $-1$
19 $[19, 19, w - 1]$ $-\frac{2}{13}e^{6} + \frac{38}{13}e^{4} - \frac{189}{13}e^{2} + \frac{174}{13}$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $-\frac{5}{26}e^{7} + \frac{41}{13}e^{5} - \frac{349}{26}e^{3} + \frac{211}{13}e$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $\phantom{-}3e$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $-\frac{3}{26}e^{7} + \frac{22}{13}e^{5} - \frac{147}{26}e^{3} + \frac{59}{13}e$
29 $[29, 29, -w + 3]$ $\phantom{-}\frac{17}{52}e^{7} - \frac{129}{26}e^{5} + \frac{911}{52}e^{3} - \frac{178}{13}e$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $\phantom{-}\frac{19}{26}e^{6} - \frac{135}{13}e^{4} + \frac{801}{26}e^{2} - \frac{118}{13}$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $-\frac{9}{13}e^{6} + \frac{132}{13}e^{4} - \frac{441}{13}e^{2} + \frac{302}{13}$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $\phantom{-}\frac{7}{52}e^{7} - \frac{47}{26}e^{5} + \frac{213}{52}e^{3} - \frac{19}{13}e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $\phantom{-}\frac{1}{52}e^{7} - \frac{3}{26}e^{5} - \frac{133}{52}e^{3} + \frac{209}{13}e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $\phantom{-}\frac{7}{26}e^{7} - \frac{47}{13}e^{5} + \frac{213}{26}e^{3} + \frac{92}{13}e$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $-\frac{7}{26}e^{7} + \frac{47}{13}e^{5} - \frac{213}{26}e^{3} - \frac{92}{13}e$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $\phantom{-}\frac{17}{52}e^{7} - \frac{129}{26}e^{5} + \frac{911}{52}e^{3} - \frac{152}{13}e$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $\phantom{-}\frac{3}{26}e^{7} - \frac{9}{13}e^{5} - \frac{217}{26}e^{3} + \frac{435}{13}e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$ $1$