Properties

Label 4.4.17725.1-19.4-d
Base field 4.4.17725.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,-w + 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,-w + 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 4x^{2} - 12x + 36\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} + e + 5$
19 $[19, 19, w + 1]$ $\phantom{-}e - 3$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{6}e^{2} + \frac{5}{3}e - 1$
19 $[19, 19, -w^{2} + 2w + 5]$ $-\frac{1}{2}e^{2} + 9$
19 $[19, 19, -w + 2]$ $-1$
25 $[25, 5, 2w^{2} - 2w - 13]$ $-\frac{1}{3}e^{2} + \frac{1}{3}e + 1$
29 $[29, 29, -w^{2} + 9]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - 5$
29 $[29, 29, -w^{2} + 2w + 6]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 2$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}4$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}e - 2$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}2e - 2$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-\frac{1}{2}e^{2} + 7$
41 $[41, 41, -w]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 6$
41 $[41, 41, -w + 1]$ $\phantom{-}\frac{1}{6}e^{2} + \frac{4}{3}e - 3$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}e - 14$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-\frac{1}{3}e^{2} + \frac{4}{3}e + 2$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-\frac{2}{3}e^{2} + \frac{5}{3}e$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{1}{3}e^{2} + \frac{7}{3}e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-w + 2]$ $1$