Properties

Label 4.4.2048.1-17.3-a
Base field \(\Q(\zeta_{16})^+\)
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17,17,-w^{3} + w^{2} + 3w - 1]$
Dimension $1$
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: $[17,17,-w^{3} + w^{2} + 3w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}2$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}6$
17 $[17, 17, -w^{3} - w^{2} + 3w + 1]$ $-2$
17 $[17, 17, w^{3} - w^{2} - 3w + 1]$ $-1$
17 $[17, 17, w^{2} - w - 3]$ $-2$
31 $[31, 31, w^{3} + w^{2} - 2w - 3]$ $-8$
31 $[31, 31, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}0$
31 $[31, 31, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}8$
31 $[31, 31, -w^{3} + w^{2} + 2w - 3]$ $\phantom{-}0$
47 $[47, 47, -2w^{3} + w^{2} + 5w - 1]$ $-8$
47 $[47, 47, 2w^{3} + w^{2} - 6w - 1]$ $-8$
47 $[47, 47, -2w^{3} + w^{2} + 6w - 1]$ $\phantom{-}8$
47 $[47, 47, 2w^{3} + w^{2} - 5w - 1]$ $\phantom{-}0$
49 $[49, 7, w^{2} + 1]$ $\phantom{-}2$
49 $[49, 7, -2w^{2} + 3]$ $-6$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $\phantom{-}0$
79 $[79, 79, -w^{3} + w^{2} + 2w - 5]$ $-8$
79 $[79, 79, w^{3} + w^{2} - 2w - 5]$ $\phantom{-}16$
79 $[79, 79, w^{3} - w^{2} - 4w - 1]$ $-16$
81 $[81, 3, -3]$ $-14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17,17,-w^{3} + w^{2} + 3w - 1]$ $1$