Properties

Label 3.3.1944.1-8.2-c
Base field 3.3.1944.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 4, w^{2} - 3w - 2]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1944.1

Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 4, w^{2} - 3w - 2]$
Dimension: $4$
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:

\(x^{4} + 3x^{3} - 6x^{2} - 21x - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2w + 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}1$
3 $[3, 3, w^{2} - w - 9]$ $\phantom{-}e$
7 $[7, 7, w^{2} - w - 7]$ $-e^{3} - 2e^{2} + 8e + 11$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{3} + e^{2} - 9e - 9$
13 $[13, 13, -2w - 1]$ $\phantom{-}e^{2} - e - 7$
17 $[17, 17, -2w^{2} + 6w + 5]$ $-e^{3} - e^{2} + 6e + 3$
31 $[31, 31, -2w^{2} + 2w + 19]$ $\phantom{-}2e + 2$
37 $[37, 37, 2w^{2} - 13]$ $-2e^{3} - 4e^{2} + 14e + 20$
41 $[41, 41, w^{2} - w - 5]$ $-e^{3} - 2e^{2} + 9e + 6$
43 $[43, 43, 2w^{2} - 2w - 17]$ $\phantom{-}3e^{3} + 4e^{2} - 25e - 28$
43 $[43, 43, -2w + 7]$ $\phantom{-}e^{3} + e^{2} - 10e - 7$
43 $[43, 43, 12w^{2} - 8w - 101]$ $\phantom{-}3e^{3} + 5e^{2} - 22e - 31$
49 $[49, 7, w^{2} + w - 1]$ $-e^{3} - 3e^{2} + 8e + 11$
59 $[59, 59, -w^{2} + w + 11]$ $\phantom{-}3e^{3} + 5e^{2} - 24e - 33$
61 $[61, 61, -w^{2} - w - 1]$ $\phantom{-}3e^{2} - 16$
79 $[79, 79, -2w^{2} + 4w + 7]$ $\phantom{-}e^{3} + 3e^{2} - 10e - 25$
83 $[83, 83, 2w - 1]$ $\phantom{-}2e^{3} + 3e^{2} - 12e - 18$
89 $[89, 89, 5w^{2} - 3w - 43]$ $\phantom{-}4e^{3} + 8e^{2} - 30e - 42$
103 $[103, 103, -2w + 5]$ $-3e^{3} - 3e^{2} + 24e + 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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