Properties

Label 3.3.361.1-19.1-a
Base field 3.3.361.1
Weight $[2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{2} + w + 4]$
Dimension $1$
CM no
Base change yes

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Base field 3.3.361.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[19, 19, -w^{2} + w + 4]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w]$ $-1$
7 $[7, 7, w^{2} - 4]$ $-1$
7 $[7, 7, w^{2} + w - 5]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}0$
11 $[11, 11, w + 1]$ $\phantom{-}3$
11 $[11, 11, -w^{2} - w + 6]$ $\phantom{-}3$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}3$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}1$
27 $[27, 3, -3]$ $\phantom{-}10$
31 $[31, 31, w^{2} - 8]$ $-4$
31 $[31, 31, 2w^{2} - 9]$ $-4$
31 $[31, 31, 2w^{2} + 2w - 9]$ $-4$
37 $[37, 37, 2w^{2} + w - 8]$ $\phantom{-}2$
37 $[37, 37, w^{2} + 2w - 6]$ $\phantom{-}2$
37 $[37, 37, w^{2} - w - 5]$ $\phantom{-}2$
83 $[83, 83, -2w - 3]$ $\phantom{-}12$
83 $[83, 83, 2w^{2} - 5]$ $\phantom{-}12$
83 $[83, 83, 2w^{2} + 2w - 13]$ $\phantom{-}12$
103 $[103, 103, 3w^{2} + 2w - 17]$ $\phantom{-}14$
103 $[103, 103, 2w^{2} - w - 5]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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