Properties

Label 4.4.12197.1-19.2-a
Base field 4.4.12197.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w + 3]$
Dimension $6$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.12197.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19, 19, -w + 3]$
Dimension: $6$
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:

\(x^{6} + 4x^{5} - 8x^{4} - 34x^{3} + 20x^{2} + 63x - 27\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}\frac{2}{53}e^{5} + \frac{18}{53}e^{4} + \frac{21}{53}e^{3} - \frac{122}{53}e^{2} - \frac{146}{53}e + \frac{138}{53}$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{2}{53}e^{5} + \frac{18}{53}e^{4} + \frac{21}{53}e^{3} - \frac{122}{53}e^{2} - \frac{146}{53}e + \frac{138}{53}$
13 $[13, 13, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{1}{53}e^{5} + \frac{9}{53}e^{4} - \frac{16}{53}e^{3} - \frac{114}{53}e^{2} + \frac{33}{53}e + \frac{175}{53}$
16 $[16, 2, 2]$ $-\frac{6}{53}e^{5} - \frac{1}{53}e^{4} + \frac{96}{53}e^{3} - \frac{5}{53}e^{2} - \frac{357}{53}e + \frac{10}{53}$
17 $[17, 17, -w^{2} + w + 3]$ $-\frac{9}{53}e^{5} - \frac{28}{53}e^{4} + \frac{91}{53}e^{3} + \frac{178}{53}e^{2} - \frac{350}{53}e - \frac{144}{53}$
19 $[19, 19, w^{3} - 5w]$ $\phantom{-}\frac{1}{53}e^{5} + \frac{9}{53}e^{4} - \frac{16}{53}e^{3} - \frac{114}{53}e^{2} + \frac{33}{53}e + \frac{175}{53}$
19 $[19, 19, -w + 3]$ $\phantom{-}1$
23 $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ $-\frac{10}{53}e^{5} - \frac{37}{53}e^{4} + \frac{54}{53}e^{3} + \frac{133}{53}e^{2} - \frac{118}{53}e + \frac{264}{53}$
23 $[23, 23, w^{2} - 2]$ $-\frac{4}{53}e^{5} - \frac{36}{53}e^{4} - \frac{42}{53}e^{3} + \frac{297}{53}e^{2} + \frac{398}{53}e - \frac{594}{53}$
25 $[25, 5, w^{2} - 3]$ $\phantom{-}\frac{6}{53}e^{5} + \frac{1}{53}e^{4} - \frac{96}{53}e^{3} + \frac{5}{53}e^{2} + \frac{304}{53}e - \frac{275}{53}$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}\frac{7}{53}e^{5} + \frac{10}{53}e^{4} - \frac{59}{53}e^{3} + \frac{50}{53}e^{2} + \frac{178}{53}e - \frac{365}{53}$
37 $[37, 37, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}\frac{6}{53}e^{5} + \frac{1}{53}e^{4} - \frac{43}{53}e^{3} + \frac{111}{53}e^{2} + \frac{39}{53}e - \frac{434}{53}$
41 $[41, 41, w^{2} - w - 5]$ $-\frac{10}{53}e^{5} - \frac{37}{53}e^{4} + \frac{54}{53}e^{3} + \frac{186}{53}e^{2} - \frac{12}{53}e + \frac{105}{53}$
47 $[47, 47, w^{3} - 6w + 1]$ $-\frac{8}{53}e^{5} - \frac{72}{53}e^{4} - \frac{31}{53}e^{3} + \frac{594}{53}e^{2} + \frac{425}{53}e - \frac{870}{53}$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{7}{53}e^{5} + \frac{10}{53}e^{4} - \frac{59}{53}e^{3} + \frac{103}{53}e^{2} + \frac{125}{53}e - \frac{842}{53}$
67 $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ $\phantom{-}\frac{18}{53}e^{5} + \frac{56}{53}e^{4} - \frac{129}{53}e^{3} - \frac{303}{53}e^{2} + \frac{223}{53}e - \frac{83}{53}$
67 $[67, 67, w^{3} - 7w + 3]$ $\phantom{-}\frac{12}{53}e^{5} + \frac{55}{53}e^{4} - \frac{86}{53}e^{3} - \frac{308}{53}e^{2} + \frac{290}{53}e - \frac{179}{53}$
73 $[73, 73, 2w^{3} - w^{2} - 9w]$ $\phantom{-}\frac{14}{53}e^{5} + \frac{20}{53}e^{4} - \frac{171}{53}e^{3} - \frac{112}{53}e^{2} + \frac{621}{53}e + \frac{277}{53}$
81 $[81, 3, -3]$ $-\frac{9}{53}e^{5} - \frac{28}{53}e^{4} + \frac{38}{53}e^{3} + \frac{125}{53}e^{2} - \frac{32}{53}e - \frac{91}{53}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w + 3]$ $-1$