Properties

Label 4.4.17725.1-19.4-c
Base field 4.4.17725.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,-w + 2]$
Dimension $2$
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: $2$
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:

\(x^{2} + 7x + 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}0$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}0$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, w + 1]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}e$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}0$
19 $[19, 19, -w + 2]$ $-1$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}2e + 6$
29 $[29, 29, -w^{2} + 9]$ $-2e - 10$
29 $[29, 29, -w^{2} + 2w + 6]$ $-e - 5$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}3e + 10$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}3e + 10$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}4$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-3e - 11$
41 $[41, 41, -w]$ $\phantom{-}2e + 14$
41 $[41, 41, -w + 1]$ $\phantom{-}2e + 14$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-e$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $\phantom{-}2e + 10$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}e + 4$
61 $[61, 61, 2w^{2} - w - 15]$ $-e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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