Properties

Label 3.3.169.1-47.1-a
Base field 3.3.169.1
Weight $[2, 2, 2]$
Level norm $47$
Level $[47, 47, 2w - 3]$
Dimension $1$
CM no
Base change no

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Base field 3.3.169.1

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

Form

Weight: $[2, 2, 2]$
Level: $[47, 47, 2w - 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $-1$
5 $[5, 5, -w^{2} + w + 2]$ $-3$
5 $[5, 5, -w + 1]$ $-3$
8 $[8, 2, 2]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}3$
27 $[27, 3, 3]$ $-2$
31 $[31, 31, -2w^{2} + 3w + 3]$ $-8$
31 $[31, 31, -w^{2} + 5]$ $-6$
31 $[31, 31, -w^{2} + 3w + 4]$ $-4$
47 $[47, 47, 2w - 3]$ $-1$
47 $[47, 47, 2w^{2} - 4w - 7]$ $-6$
47 $[47, 47, 2w^{2} - 2w - 3]$ $\phantom{-}2$
53 $[53, 53, 3w^{2} - 4w - 8]$ $\phantom{-}5$
53 $[53, 53, 4w^{2} - 6w - 11]$ $-11$
53 $[53, 53, 3w^{2} - 5w - 6]$ $\phantom{-}13$
73 $[73, 73, w^{2} - 4w - 4]$ $-3$
73 $[73, 73, 2w^{2} - w - 8]$ $-1$
73 $[73, 73, 3w^{2} - 5w - 5]$ $-9$
79 $[79, 79, -3w^{2} + 5w + 4]$ $-8$
79 $[79, 79, 2w^{2} - w - 9]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47, 47, 2w - 3]$ $1$