Properties

Label 3.3.148.1-52.1-a
Base field 3.3.148.1
Weight $[2, 2, 2]$
Level norm $52$
Level $[52, 26, -w^{2} - 2w + 3]$
Dimension $1$
CM no
Base change no

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Base field 3.3.148.1

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

Form

Weight: $[2, 2, 2]$
Level: $[52, 26, -w^{2} - 2w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $1$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}0$
5 $[5, 5, -w^{2} + w + 1]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + 2w + 2]$ $-1$
17 $[17, 17, 2w + 1]$ $-2$
19 $[19, 19, -w^{2} + 2w + 4]$ $-4$
23 $[23, 23, -w^{2} - w + 3]$ $\phantom{-}0$
25 $[25, 5, -2w^{2} + w + 4]$ $\phantom{-}6$
27 $[27, 3, 3]$ $\phantom{-}4$
29 $[29, 29, w^{2} - 3w - 1]$ $-2$
31 $[31, 31, 2w^{2} - 2w - 3]$ $\phantom{-}8$
37 $[37, 37, w^{2} + w - 5]$ $\phantom{-}6$
37 $[37, 37, w - 4]$ $-6$
43 $[43, 43, 2w^{2} - w - 2]$ $\phantom{-}4$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-4$
61 $[61, 61, -3w^{2} + 4w + 4]$ $\phantom{-}6$
67 $[67, 67, -w - 4]$ $-4$
67 $[67, 67, -3w^{2} + 8]$ $\phantom{-}4$
67 $[67, 67, w^{2} - 3w - 3]$ $-12$
79 $[79, 79, w^{2} + 2w - 4]$ $\phantom{-}0$
89 $[89, 89, 3w^{2} - 3w - 5]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 1]$ $-1$
$13$ $[13, 13, -w^{2} + 2w + 2]$ $1$