Properties

Label 4.4.15317.1-16.5-b
Base field 4.4.15317.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16,4,w^{3} - 2w^{2} - 2w + 1]$
Dimension $5$
CM no
Base change no

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Base field 4.4.15317.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16,4,w^{3} - 2w^{2} - 2w + 1]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 8x^{3} + 14x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, -w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} + w + 1]$ $-1$
19 $[19, 19, -w^{3} + 5w + 3]$ $-2e^{2} + 4$
19 $[19, 19, w^{3} - 3w^{2} - 2w + 7]$ $-2e$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ $-2e^{3} + 8e + 2$
43 $[43, 43, -w^{3} + w^{2} + 2w - 1]$ $\phantom{-}3e^{3} - e^{2} - 12e + 2$
43 $[43, 43, w^{3} - 2w^{2} - w + 1]$ $-3e^{3} + 3e^{2} + 12e - 12$
43 $[43, 43, -w^{3} + 5w + 1]$ $\phantom{-}2e^{2} - 2e - 8$
47 $[47, 47, -w^{3} + w^{2} + 2w + 1]$ $\phantom{-}e^{3} + 3e^{2} - 2e - 12$
47 $[47, 47, w^{3} - 5w - 5]$ $-e^{4} + 2e^{3} + 6e^{2} - 9e - 6$
47 $[47, 47, -w^{3} + 3w^{2} + 2w - 9]$ $-e^{4} + 4e^{2} + e$
47 $[47, 47, w^{3} - 2w^{2} - w + 3]$ $-3e^{3} + e^{2} + 12e - 4$
49 $[49, 7, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}3e^{3} - e^{2} - 14e$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 7]$ $\phantom{-}2e^{4} - e^{3} - 13e^{2} + 2e + 12$
53 $[53, 53, 2w - 1]$ $-2e^{4} + 12e^{2} - 12$
67 $[67, 67, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}e^{4} - 2e^{3} - 4e^{2} + 7e - 4$
67 $[67, 67, -w^{3} + 2w^{2} + 3w - 1]$ $-3e^{4} + 16e^{2} + 3e - 10$
81 $[81, 3, -3]$ $-e^{4} + 4e^{2} + e + 4$
83 $[83, 83, 2w^{3} - 4w^{2} - 6w + 9]$ $\phantom{-}e^{4} - 6e^{2} + 3e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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