Properties

Label 4.4.11197.1-19.1-d
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$
Dimension: $2$
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:

\(x^{2} + 3x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}e + 1$
11 $[11, 11, -w - 2]$ $-3e - 5$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}2e + 1$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}5e + 6$
16 $[16, 2, 2]$ $\phantom{-}4e + 8$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}1$
23 $[23, 23, -w^{2} + w + 3]$ $-4e - 5$
23 $[23, 23, -w^{2} + 3]$ $-4e - 7$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-2e + 4$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $-2e - 3$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-2e - 8$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-3e - 14$
47 $[47, 47, w^{2} - 3w - 2]$ $-3$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}8e + 9$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $-5e - 7$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $-5e - 7$
83 $[83, 83, -2w + 3]$ $\phantom{-}10e + 19$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $\phantom{-}6e + 19$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}2e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $-1$