Properties

Label 4.4.10889.1-17.1-a
Base field 4.4.10889.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{3} + w^{2} + 5w]$
Dimension $4$
CM no
Base change no

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Base field 4.4.10889.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{3} + w^{2} + 5w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 4x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
7 $[7, 7, -w + 2]$ $-e^{3} + 3e$
8 $[8, 2, -w^{3} + 5w + 3]$ $-e$
11 $[11, 11, w^{3} - w^{2} - 5w + 4]$ $-e^{2} - 1$
11 $[11, 11, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{3} - 3e$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}1$
25 $[25, 5, -w^{2} + w + 3]$ $-2e$
25 $[25, 5, -w^{2} + 2]$ $-2e^{3} + 4e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $\phantom{-}5e^{3} - 15e$
29 $[29, 29, -w^{3} + 4w + 2]$ $-5e^{3} + 21e$
37 $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ $\phantom{-}2e^{2} - 6$
43 $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ $\phantom{-}5e^{3} - 19e$
47 $[47, 47, -w^{3} + 6w]$ $-e^{3} + 9e$
53 $[53, 53, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}e^{2} + 1$
81 $[81, 3, -3]$ $\phantom{-}5e^{2} - 15$
83 $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ $\phantom{-}2e^{2} - 16$
89 $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}4e^{2} - 12$
89 $[89, 89, 2w - 3]$ $-2e^{3} + 8e$
101 $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ $-10e^{2} + 20$
107 $[107, 107, -w^{3} + w^{2} + 4w - 5]$ $-5e^{2} + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{3} + w^{2} + 5w]$ $-1$