Properties

Label 4.4.12725.1-19.2-c
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,w^{2} - 6]$
Dimension $3$
CM no
Base change no

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Base field 4.4.12725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,w^{2} - 6]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 2x^{2} - 22x + 58\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}2e^{2} + 2e - 32$
11 $[11, 11, w^{2} - 5]$ $-2$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e^{2} + e - 14$
11 $[11, 11, w - 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}e^{2} + 2e - 19$
19 $[19, 19, w^{2} - 2w - 5]$ $-2e^{2} - 3e + 38$
19 $[19, 19, -w^{2} + 6]$ $-1$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}e^{2} - 18$
29 $[29, 29, w]$ $\phantom{-}e^{2} + e - 13$
29 $[29, 29, 2w^{2} - w - 10]$ $-2e^{2} - 2e + 35$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-2e^{2} - 3e + 39$
29 $[29, 29, w - 1]$ $-e + 1$
31 $[31, 31, w^{3} - 6w - 6]$ $-6$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}2e^{2} + 4e - 36$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-2e^{2} - 2e + 39$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}e^{2} - 17$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-e^{2} - e + 16$
59 $[59, 59, 2w^{2} - w - 13]$ $-3e^{2} - 3e + 46$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}e^{2} + 2e - 25$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}3e^{2} + 5e - 51$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,w^{2} - 6]$ $1$