Properties

Label 4.4.13725.1-19.1-b
Base field 4.4.13725.1
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 4.4.13725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + x + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19, 19, -w - 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 37x^{4} + 351x^{2} - 243\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ $-\frac{1}{12}e^{4} + \frac{11}{6}e^{2} - \frac{23}{4}$
11 $[11, 11, w^{2} - w - 8]$ $\phantom{-}e$
11 $[11, 11, -4w^{3} + 13w^{2} + 23w - 55]$ $\phantom{-}\frac{1}{108}e^{5} - \frac{5}{54}e^{3} - \frac{5}{4}e$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} + \frac{7}{2}$
19 $[19, 19, -w - 1]$ $\phantom{-}1$
19 $[19, 19, -w^{3} + 3w^{2} + 7w - 14]$ $\phantom{-}\frac{1}{6}e^{4} - \frac{19}{6}e^{2} + 2$
19 $[19, 19, w^{3} - 4w^{2} - 5w + 20]$ $-\frac{1}{12}e^{4} + \frac{11}{6}e^{2} - \frac{19}{4}$
19 $[19, 19, -3w^{3} + 10w^{2} + 17w - 43]$ $-\frac{1}{2}e^{2} + \frac{13}{2}$
25 $[25, 5, -w^{3} + 3w^{2} + 6w - 10]$ $\phantom{-}\frac{1}{6}e^{4} - \frac{19}{6}e^{2} - 1$
29 $[29, 29, 4w^{3} - 13w^{2} - 23w + 57]$ $\phantom{-}\frac{1}{108}e^{5} - \frac{16}{27}e^{3} + \frac{25}{4}e$
29 $[29, 29, w^{2} - w - 6]$ $\phantom{-}\frac{1}{36}e^{5} - \frac{7}{9}e^{3} + \frac{19}{4}e$
31 $[31, 31, -2w^{3} + 7w^{2} + 11w - 31]$ $-\frac{1}{12}e^{4} + \frac{11}{6}e^{2} - \frac{7}{4}$
31 $[31, 31, -2w^{3} + 7w^{2} + 11w - 32]$ $-\frac{1}{12}e^{4} + \frac{11}{6}e^{2} - \frac{43}{4}$
41 $[41, 41, 3w^{3} - 10w^{2} - 18w + 43]$ $\phantom{-}\frac{1}{54}e^{5} - \frac{37}{54}e^{3} + 8e$
41 $[41, 41, 3w^{3} - 9w^{2} - 19w + 37]$ $\phantom{-}\frac{1}{36}e^{5} - \frac{7}{9}e^{3} + \frac{11}{4}e$
41 $[41, 41, 2w^{3} - 6w^{2} - 11w + 24]$ $-\frac{7}{108}e^{5} + \frac{89}{54}e^{3} - \frac{37}{4}e$
41 $[41, 41, -2w^{3} + 7w^{2} + 12w - 33]$ $-\frac{1}{27}e^{5} + \frac{37}{27}e^{3} - 13e$
59 $[59, 59, 3w^{3} - 10w^{2} - 17w + 46]$ $-\frac{7}{108}e^{5} + \frac{31}{27}e^{3} + \frac{5}{4}e$
59 $[59, 59, -w^{3} + 4w^{2} + 5w - 17]$ $-\frac{1}{54}e^{5} + \frac{37}{54}e^{3} - 7e$
61 $[61, 61, 4w^{3} - 12w^{2} - 25w + 50]$ $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + \frac{23}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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