Properties

Label 4.4.11348.1-16.5-a
Base field 4.4.11348.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 16, -w^{2} + 2w]$
Dimension $2$
CM no
Base change no

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Base field 4.4.11348.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 16, -w^{2} + 2w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e + 2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}2$
19 $[19, 19, -2w + 1]$ $-4$
29 $[29, 29, -w^{3} + w^{2} + 2w - 1]$ $-2$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ $-2e - 2$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 5]$ $-2$
43 $[43, 43, -2w^{3} + 2w^{2} + 8w + 3]$ $\phantom{-}4e$
43 $[43, 43, -w^{2} + 3w + 1]$ $\phantom{-}2e + 6$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}0$
53 $[53, 53, -w^{3} + w^{2} + 6w + 1]$ $-2e + 4$
59 $[59, 59, 2w^{3} - 2w^{2} - 10w + 3]$ $-2e - 6$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}2e - 8$
61 $[61, 61, w^{2} + w - 3]$ $-2$
71 $[71, 71, -w^{3} + 5w + 1]$ $-8$
71 $[71, 71, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}4e + 4$
81 $[81, 3, -3]$ $\phantom{-}4e + 6$
83 $[83, 83, -3w^{3} + 5w^{2} + 12w - 9]$ $\phantom{-}8e + 4$
83 $[83, 83, -3w^{3} + 6w^{2} + 13w - 13]$ $\phantom{-}2e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$