Properties

Label 4.4.16357.1-16.1-a
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.16357.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 9x^{6} + 25x^{4} - 21x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 5w + 2]$ $-e^{7} + 8e^{5} - 18e^{3} + 9e$
5 $[5, 5, w - 1]$ $\phantom{-}e^{2} - 4$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}e^{5} - 7e^{3} + 12e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}e^{7} - 8e^{5} + 20e^{3} - 17e$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}e^{7} - 10e^{5} + 29e^{3} - 22e$
25 $[25, 5, -w^{2} + w + 3]$ $-e^{7} + 10e^{5} - 27e^{3} + 14e$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $\phantom{-}e^{7} - 8e^{5} + 18e^{3} - 12e$
31 $[31, 31, -w - 3]$ $-e^{6} + 4e^{4} - 2$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-e^{3} + 4e$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}2e^{5} - 11e^{3} + 13e$
43 $[43, 43, w^{3} - 7w - 2]$ $-e^{6} + 8e^{4} - 17e^{2}$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-e^{7} + 6e^{5} - 10e^{3} + 5e$
61 $[61, 61, w^{2} - 3]$ $-3e^{7} + 24e^{5} - 57e^{3} + 39e$
67 $[67, 67, w^{2} + w - 4]$ $-4e^{6} + 26e^{4} - 45e^{2} + 16$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}e^{7} - 8e^{5} + 20e^{3} - 11e$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $\phantom{-}e^{6} - 6e^{4} + 13e^{2} - 14$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}4e^{6} - 28e^{4} + 49e^{2} - 16$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}2e^{7} - 23e^{5} + 76e^{3} - 62e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $-1$