Properties

Label 4.4.7600.1-19.3-a
Base field 4.4.7600.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,-w^{2} + w + 6]$
Dimension $1$
CM no
Base change no

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Base field 4.4.7600.1

Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,-w^{2} + w + 6]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + w^{2} + 5w - 6]$ $\phantom{-}1$
9 $[9, 3, -w^{2} - w + 4]$ $\phantom{-}4$
9 $[9, 3, w^{2} - w - 4]$ $\phantom{-}4$
11 $[11, 11, w + 1]$ $\phantom{-}0$
11 $[11, 11, w - 1]$ $\phantom{-}3$
19 $[19, 19, -w]$ $-1$
19 $[19, 19, -w^{2} - w + 6]$ $-2$
19 $[19, 19, -w^{2} + w + 6]$ $-1$
25 $[25, 5, 2w^{2} - 9]$ $-2$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{3} + 4w - 2]$ $\phantom{-}3$
41 $[41, 41, 2w^{2} - w - 7]$ $\phantom{-}0$
41 $[41, 41, w^{3} - w^{2} - 6w + 4]$ $-6$
61 $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ $\phantom{-}13$
61 $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ $\phantom{-}14$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ $-10$
61 $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ $\phantom{-}1$
89 $[89, 89, -w^{3} + w^{2} + 6w - 9]$ $\phantom{-}0$
89 $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ $-15$
109 $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ $-20$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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