Properties

Label 4.4.12197.1-19.1-b
Base field 4.4.12197.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, w^{3} - 5w]$
Dimension $4$
CM no
Base change no

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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: $[19, 19, w^{3} - 5w]$
Dimension: $4$
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:

\(x^{4} - 16x^{2} + 52\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $-\frac{1}{2}e^{2} + 4$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e + 3$
13 $[13, 13, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{2}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{5}{2}e - 2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{2}e^{2} - e - 5$
19 $[19, 19, w^{3} - 5w]$ $\phantom{-}1$
19 $[19, 19, -w + 3]$ $\phantom{-}\frac{1}{2}e^{2} - 8$
23 $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e + 6$
23 $[23, 23, w^{2} - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 4e - 2$
25 $[25, 5, w^{2} - 3]$ $-\frac{1}{4}e^{3} + e^{2} + \frac{5}{2}e - 9$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{5}{2}e + 1$
37 $[37, 37, -w^{3} + w^{2} + 6w - 4]$ $-\frac{1}{4}e^{3} + \frac{5}{2}e - 6$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - 2$
47 $[47, 47, w^{3} - 6w + 1]$ $-\frac{1}{2}e^{2}$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 4e$
67 $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ $\phantom{-}\frac{3}{4}e^{3} - \frac{3}{2}e^{2} - \frac{13}{2}e + 13$
67 $[67, 67, w^{3} - 7w + 3]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 5e - 10$
73 $[73, 73, 2w^{3} - w^{2} - 9w]$ $\phantom{-}\frac{3}{2}e^{2} - e - 7$
81 $[81, 3, -3]$ $-\frac{1}{4}e^{3} + e^{2} + \frac{1}{2}e - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{3} - 5w]$ $-1$