Properties

Label 4.4.11324.1-16.2-e
Base field 4.4.11324.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 4, -w^{3} + w^{2} + 4w - 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.11324.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 4, -w^{3} + w^{2} + 4w - 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 3x^{2} - 5x - 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-e - 2$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}5$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e^{2} + 2e - 6$
19 $[19, 19, -w^{3} + 3w - 1]$ $\phantom{-}e^{2} - 5$
23 $[23, 23, -w + 3]$ $\phantom{-}2e^{2} + 2e - 10$
31 $[31, 31, -w^{2} - 2w + 1]$ $-e^{2} - 2e + 1$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}e + 8$
43 $[43, 43, 2w - 1]$ $\phantom{-}e^{2} + 2e - 5$
53 $[53, 53, -w - 3]$ $\phantom{-}e^{2} + 3e - 1$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{2} + 3e - 1$
61 $[61, 61, w^{3} - 3w - 5]$ $\phantom{-}e^{2} - e - 11$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $\phantom{-}e^{2} - 11$
81 $[81, 3, -3]$ $-3e^{2} + 22$
83 $[83, 83, -w^{3} + 5w - 3]$ $-2e^{2} + 8$
89 $[89, 89, w^{2} + 1]$ $\phantom{-}2e^{2} + 4e - 12$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $-4e^{2} - 6e + 15$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $-2e^{2} + 13$
97 $[97, 97, w^{3} - 3w - 3]$ $-2e^{2} + e + 20$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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