Properties

Label 4.4.1957.1-43.2-a
Base field 4.4.1957.1
Weight $[2, 2, 2, 2]$
Level norm $43$
Level $[43, 43, -w^{2} + 2w + 3]$
Dimension $4$
CM no
Base change no

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Base field 4.4.1957.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[43, 43, -w^{2} + 2w + 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 9x^{2} + 2x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 3w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e^{3} - 9e + 2$
16 $[16, 2, 2]$ $\phantom{-}e^{3} - 10e + 4$
19 $[19, 19, -w^{3} + w^{2} + 4w]$ $-2$
23 $[23, 23, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}2e^{3} - 16e + 4$
27 $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ $-2e^{3} - e^{2} + 18e + 1$
31 $[31, 31, -w^{3} + 5w]$ $-2e^{3} + 18e$
37 $[37, 37, -w^{3} + 5w + 1]$ $-2e^{3} - e^{2} + 18e$
43 $[43, 43, w^{2} + w - 3]$ $-2e^{2} + 10$
43 $[43, 43, -w^{2} + 2w + 3]$ $-1$
47 $[47, 47, -w^{3} + w^{2} + 2w + 2]$ $-2e^{3} + 16e + 2$
47 $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ $-2e^{3} - e^{2} + 14e + 4$
53 $[53, 53, -w^{3} + w^{2} + 2w - 3]$ $-2e^{3} + 14e - 6$
59 $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ $-3e^{3} + 25e - 2$
59 $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ $-2e^{3} + e^{2} + 20e - 7$
61 $[61, 61, -w^{3} + w^{2} + w - 2]$ $\phantom{-}4e^{3} + e^{2} - 34e + 3$
67 $[67, 67, 2w^{3} - 5w - 2]$ $\phantom{-}e^{2} - 4e - 9$
71 $[71, 71, 2w^{2} - w - 3]$ $-4e^{3} + 34e - 6$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}2e$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ $-2e^{2} - 4e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43, 43, -w^{2} + 2w + 3]$ $1$