Properties

Label 4.4.7537.1-16.1-d
Base field 4.4.7537.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $1$
CM no
Base change no

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Base field 4.4.7537.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $-1$
3 $[3, 3, w]$ $\phantom{-}1$
8 $[8, 2, -w^{3} + 5w + 1]$ $-1$
19 $[19, 19, w^{3} - w^{2} - 3w + 2]$ $\phantom{-}5$
19 $[19, 19, -w^{3} + 4w - 2]$ $\phantom{-}0$
23 $[23, 23, w^{3} + w^{2} - 4w - 5]$ $\phantom{-}4$
27 $[27, 3, -w^{3} + w^{2} + 5w - 4]$ $\phantom{-}7$
31 $[31, 31, w^{3} + w^{2} - 4w - 1]$ $-2$
47 $[47, 47, -w^{2} - w + 5]$ $-2$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 10]$ $-4$
59 $[59, 59, 2w - 1]$ $\phantom{-}5$
59 $[59, 59, w^{3} - 2w - 2]$ $-5$
61 $[61, 61, -w^{2} - 2w + 4]$ $-12$
67 $[67, 67, 2w^{2} - 7]$ $\phantom{-}13$
73 $[73, 73, 5w^{3} + w^{2} - 23w - 8]$ $-9$
79 $[79, 79, -2w^{3} - w^{2} + 9w + 7]$ $\phantom{-}10$
79 $[79, 79, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}10$
79 $[79, 79, w^{3} - w^{2} - w - 2]$ $\phantom{-}10$
79 $[79, 79, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}10$
83 $[83, 83, w^{3} + w^{2} - 3w - 4]$ $-16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 1]$ $1$
$8$ $[8, 2, -w^{3} + 5w + 1]$ $1$