Properties

Label 3.3.469.1-19.1-a
Base field 3.3.469.1
Weight $[2, 2, 2]$
Level norm $19$
Level $[19, 19, w^{2} - 7]$
Dimension $1$
CM no
Base change no

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Base field 3.3.469.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[19, 19, w^{2} - 7]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}1$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}3$
7 $[7, 7, w + 1]$ $\phantom{-}4$
7 $[7, 7, -w + 3]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}0$
17 $[17, 17, w + 3]$ $-6$
19 $[19, 19, w^{2} - 7]$ $\phantom{-}1$
27 $[27, 3, 3]$ $\phantom{-}8$
43 $[43, 43, -2w - 5]$ $-8$
47 $[47, 47, 2w + 3]$ $\phantom{-}8$
53 $[53, 53, 3w^{2} + 2w - 9]$ $-2$
59 $[59, 59, 2w^{2} + w - 5]$ $-4$
61 $[61, 61, 3w - 1]$ $-14$
61 $[61, 61, 2w^{2} + w - 9]$ $-6$
61 $[61, 61, 2w^{2} - w - 7]$ $-14$
67 $[67, 67, -2w^{2} + 13]$ $\phantom{-}4$
67 $[67, 67, -3w - 7]$ $\phantom{-}0$
73 $[73, 73, w^{2} + 2w - 5]$ $\phantom{-}6$
79 $[79, 79, w - 5]$ $\phantom{-}0$
83 $[83, 83, -2w^{2} + 4w + 3]$ $\phantom{-}4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{2} - 7]$ $-1$