Properties

Label 4.4.2048.1-47.3-a
Base field \(\Q(\zeta_{16})^+\)
Weight $[2, 2, 2, 2]$
Level norm $47$
Level $[47,47,-w^{3} - w^{2} + 5w + 3]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\zeta_{16})^+\)

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

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
17 $[17, 17, -w^{2} - w + 3]$ $-4e + 4$
17 $[17, 17, -w^{3} - w^{2} + 3w + 1]$ $\phantom{-}2e - 5$
17 $[17, 17, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e$
17 $[17, 17, w^{2} - w - 3]$ $-2$
31 $[31, 31, w^{3} + w^{2} - 2w - 3]$ $\phantom{-}2e + 3$
31 $[31, 31, -w^{3} + w^{2} + 4w - 1]$ $-e + 4$
31 $[31, 31, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}6$
31 $[31, 31, -w^{3} + w^{2} + 2w - 3]$ $-2e + 2$
47 $[47, 47, -2w^{3} + w^{2} + 5w - 1]$ $-4e$
47 $[47, 47, 2w^{3} + w^{2} - 6w - 1]$ $\phantom{-}8$
47 $[47, 47, -2w^{3} + w^{2} + 6w - 1]$ $-1$
47 $[47, 47, 2w^{3} + w^{2} - 5w - 1]$ $-6$
49 $[49, 7, w^{2} + 1]$ $\phantom{-}e - 2$
49 $[49, 7, -2w^{2} + 3]$ $-2e + 6$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $\phantom{-}2e - 3$
79 $[79, 79, -w^{3} + w^{2} + 2w - 5]$ $-2e + 10$
79 $[79, 79, w^{3} + w^{2} - 2w - 5]$ $-e - 2$
79 $[79, 79, w^{3} - w^{2} - 4w - 1]$ $-8e + 5$
81 $[81, 3, -3]$ $\phantom{-}2e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47,47,-w^{3} - w^{2} + 5w + 3]$ $1$