Properties

Label 4.4.13676.1-4.1-a
Base field 4.4.13676.1
Weight $[2, 2, 2, 2]$
Level norm $4$
Level $[4, 2, w^{3} - 5w]$
Dimension $3$
CM no
Base change no

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Base field 4.4.13676.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - 9x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} - w + 3]$ $-1$
5 $[5, 5, w^{3} - 5w + 1]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 6w - 2]$ $-e^{2} - e + 6$
13 $[13, 13, -w^{2} + 4]$ $-e - 4$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $\phantom{-}e^{2} + 2e - 6$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $-3e - 4$
37 $[37, 37, -w^{3} + 6w - 4]$ $-e - 4$
41 $[41, 41, -w^{3} + 5w - 5]$ $-e^{2} - 4e + 6$
43 $[43, 43, w^{3} - 4w + 4]$ $\phantom{-}e^{2} + e - 10$
43 $[43, 43, -2w^{3} + 11w - 2]$ $\phantom{-}e^{2} - e - 10$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $-e^{2} + e + 6$
47 $[47, 47, 2w - 1]$ $-2e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $-10$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $-2e$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $\phantom{-}e^{2} + 5e - 6$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $-2e^{2} - 4e + 8$
81 $[81, 3, -3]$ $\phantom{-}2e^{2} + 5e - 8$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $-e^{2} - 3e + 6$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}2e^{2} + 3e - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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