Properties

Label 4.4.7537.1-16.2-c
Base field 4.4.7537.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 16, w^{2} + w - 4]$
Dimension $3$
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: $[16, 16, w^{2} + w - 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 9x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}e$
8 $[8, 2, -w^{3} + 5w + 1]$ $-e^{2} + e + 5$
19 $[19, 19, w^{3} - w^{2} - 3w + 2]$ $-e$
19 $[19, 19, -w^{3} + 4w - 2]$ $\phantom{-}4$
23 $[23, 23, w^{3} + w^{2} - 4w - 5]$ $-e^{2} + 8$
27 $[27, 3, -w^{3} + w^{2} + 5w - 4]$ $\phantom{-}4$
31 $[31, 31, w^{3} + w^{2} - 4w - 1]$ $-e - 4$
47 $[47, 47, -w^{2} - w + 5]$ $-e^{2} + 4e + 8$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 10]$ $-2e^{2} + e + 10$
59 $[59, 59, 2w - 1]$ $\phantom{-}2e + 4$
59 $[59, 59, w^{3} - 2w - 2]$ $-2e^{2} + 12$
61 $[61, 61, -w^{2} - 2w + 4]$ $\phantom{-}2e^{2} - 10$
67 $[67, 67, 2w^{2} - 7]$ $\phantom{-}2e^{2} - 4e - 12$
73 $[73, 73, 5w^{3} + w^{2} - 23w - 8]$ $\phantom{-}2e^{2} + 2e - 14$
79 $[79, 79, -2w^{3} - w^{2} + 9w + 7]$ $-4e$
79 $[79, 79, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}2e - 8$
79 $[79, 79, w^{3} - w^{2} - w - 2]$ $\phantom{-}e^{2} + 4e - 8$
79 $[79, 79, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}e + 4$
83 $[83, 83, w^{3} + w^{2} - 3w - 4]$ $\phantom{-}2e^{2} - 4e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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