Properties

Label 4.4.12725.1-19.1-a
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, w^{2} - 2w - 5]$
Dimension $1$
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: $[19, 19, w^{2} - 2w - 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}0$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}2$
11 $[11, 11, -w^{2} + 2w + 4]$ $-1$
11 $[11, 11, w - 2]$ $\phantom{-}3$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, w^{2} - 2w - 5]$ $-1$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}4$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}1$
29 $[29, 29, w]$ $\phantom{-}8$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}5$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-4$
29 $[29, 29, w - 1]$ $\phantom{-}2$
31 $[31, 31, w^{3} - 6w - 6]$ $-5$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}10$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-10$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}2$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}10$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}7$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}8$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{2} - 2w - 5]$ $1$