Properties

Label 4.4.17428.1-12.1-e
Base field 4.4.17428.1
Weight $[2, 2, 2, 2]$
Level norm $12$
Level $[12, 6, w^{2} - 2w]$
Dimension $3$
CM no
Base change no

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Base field 4.4.17428.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[12, 6, w^{2} - 2w]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 6x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}1$
27 $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ $-e^{2} - e$
29 $[29, 29, w^{3} + w^{2} - 2w - 1]$ $\phantom{-}e^{2} - 2e - 1$
31 $[31, 31, -w^{2} - w + 1]$ $-e + 3$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ $\phantom{-}e^{2} - e - 6$
37 $[37, 37, -w^{3} + 3w + 1]$ $\phantom{-}3e^{2} + e - 12$
41 $[41, 41, -w^{2} + w + 5]$ $-2e^{2} - e + 11$
41 $[41, 41, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}e^{2} + 2e - 9$
43 $[43, 43, -2w - 1]$ $-3e^{2} + 2e + 9$
47 $[47, 47, w^{2} + w - 5]$ $\phantom{-}e^{2} - 1$
47 $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ $-e^{2} + 3e + 8$
53 $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ $\phantom{-}2e^{2} + 2e - 6$
59 $[59, 59, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}e^{2} + 5e - 4$
59 $[59, 59, w^{3} + w^{2} - 4w - 5]$ $\phantom{-}e^{2} - 2e - 7$
71 $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ $\phantom{-}2e^{2} - 2e - 12$
71 $[71, 71, w^{2} + 3w + 1]$ $\phantom{-}e^{2} - 2e - 3$
73 $[73, 73, w^{3} - 5w + 1]$ $-e^{2} + e + 4$
89 $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ $-e^{2} + 2e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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