Properties

Label 4.4.10025.1-19.2-e
Base field 4.4.10025.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,w - 1]$
Dimension $6$
CM no
Base change no

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Base field 4.4.10025.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 10x + 20\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,w - 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{6} + 4x^{5} - 8x^{4} - 50x^{3} - 48x^{2} + 16x + 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{11}{4}e^{3} - \frac{25}{4}e^{2} - 2e + \frac{1}{4}$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{11}{2}e^{3} + \frac{27}{2}e^{2} + 3e - \frac{9}{2}$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{13}{4}e^{3} + \frac{25}{4}e^{2} - 3e - \frac{7}{4}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $-\frac{3}{4}e^{5} - e^{4} + \frac{37}{4}e^{3} + \frac{55}{4}e^{2} - \frac{15}{2}e - \frac{7}{4}$
19 $[19, 19, w - 1]$ $-1$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{13}{2}e^{3} + \frac{27}{2}e^{2} - 6e - \frac{17}{2}$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 6e^{2} + \frac{15}{2}e - \frac{5}{2}$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $-e^{5} - \frac{9}{4}e^{4} + \frac{47}{4}e^{3} + \frac{57}{2}e^{2} + \frac{3}{4}e - \frac{43}{4}$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $-\frac{7}{4}e^{5} - \frac{17}{4}e^{4} + 20e^{3} + \frac{217}{4}e^{2} + \frac{25}{4}e - \frac{43}{2}$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}\frac{3}{2}e^{5} + \frac{7}{2}e^{4} - 17e^{3} - \frac{91}{2}e^{2} - \frac{15}{2}e + 13$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $-\frac{5}{4}e^{5} - 3e^{4} + \frac{55}{4}e^{3} + \frac{157}{4}e^{2} + \frac{17}{2}e - \frac{45}{4}$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{9}{4}e^{3} - \frac{25}{4}e^{2} - 6e + \frac{15}{4}$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $\phantom{-}\frac{5}{4}e^{5} + \frac{7}{4}e^{4} - 15e^{3} - \frac{103}{4}e^{2} + \frac{33}{4}e + \frac{29}{2}$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-\frac{1}{2}e^{5} - \frac{3}{2}e^{4} + 5e^{3} + \frac{37}{2}e^{2} + \frac{21}{2}e + 2$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + 2e^{3} + \frac{39}{4}e^{2} + \frac{43}{4}e - \frac{1}{2}$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $-\frac{1}{2}e^{5} - \frac{7}{4}e^{4} + \frac{23}{4}e^{3} + 20e^{2} + \frac{13}{4}e + \frac{1}{4}$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $-e^{5} - e^{4} + 12e^{3} + 15e^{2} - 11e - 2$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{4}e^{5} + \frac{7}{4}e^{4} - \frac{17}{2}e^{3} - \frac{93}{4}e^{2} - \frac{3}{4}e + 9$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}e^{3} - e^{2} - 11e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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