Properties

Label 3.3.621.1-12.1-b
Base field 3.3.621.1
Weight $[2, 2, 2]$
Level norm $12$
Level $[12, 6, w^{2} - w - 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.621.1

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

Form

Weight: $[2, 2, 2]$
Level: $[12, 6, w^{2} - w - 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $5$

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 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $\phantom{-}1$
4 $[4, 2, -w^{2} + w + 5]$ $-1$
7 $[7, 7, -w + 2]$ $-e^{2} + e + 4$
19 $[19, 19, -2w^{2} + w + 10]$ $\phantom{-}e^{2} + e - 2$
23 $[23, 23, -w^{2} + 8]$ $\phantom{-}2e - 2$
23 $[23, 23, -w^{2} + 2]$ $-e^{2} - e + 6$
29 $[29, 29, -w^{2} + 2w + 4]$ $-3e^{2} - e + 10$
37 $[37, 37, w^{2} - 2w - 8]$ $-2e + 4$
41 $[41, 41, 4w^{2} - 3w - 20]$ $\phantom{-}e^{2} - 3e - 8$
43 $[43, 43, -w - 4]$ $\phantom{-}e^{2} - 3e - 6$
47 $[47, 47, 2w - 1]$ $-e^{2} + e + 4$
49 $[49, 7, -2w^{2} + 3w + 4]$ $\phantom{-}2e + 4$
59 $[59, 59, 2w^{2} - 13]$ $-2e + 6$
61 $[61, 61, -3w^{2} + 4w + 10]$ $\phantom{-}2e^{2} + 4e - 8$
67 $[67, 67, 2w^{2} - 2w - 7]$ $-2e^{2} + 6$
71 $[71, 71, -3w - 4]$ $\phantom{-}4e^{2} + 4e - 16$
79 $[79, 79, 2w^{2} - 3w - 8]$ $\phantom{-}2e^{2} + 2e - 4$
83 $[83, 83, 2w^{2} - w - 14]$ $-2e - 10$
83 $[83, 83, -4w^{2} + 3w + 22]$ $\phantom{-}4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$
$4$ $[4, 2, -w^{2} + w + 5]$ $1$