Properties

Label 3.3.404.1-36.1-b
Base field 3.3.404.1
Weight $[2, 2, 2]$
Level norm $36$
Level $[36, 6, -w^{2} + 5]$
Dimension $3$
CM no
Base change no

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Base field 3.3.404.1

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

Form

Weight: $[2, 2, 2]$
Level: $[36, 6, -w^{2} + 5]$
Dimension: $3$
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:

\(x^{3} - 10x + 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}0$
3 $[3, 3, w^{2} - 2w - 2]$ $\phantom{-}e$
7 $[7, 7, -w + 2]$ $\phantom{-}e + 2$
9 $[9, 3, w^{2} - 2]$ $-1$
11 $[11, 11, -w^{2} + 2w + 4]$ $-e^{2} - 2e + 8$
29 $[29, 29, -2w + 1]$ $\phantom{-}3e$
37 $[37, 37, 2w^{2} - 4w - 3]$ $-e^{2} + 6$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}2e^{2} + e - 12$
37 $[37, 37, 2w^{2} - w - 8]$ $-e + 6$
41 $[41, 41, w^{2} - 4w + 2]$ $-e + 2$
43 $[43, 43, -2w^{2} + 2w + 7]$ $-2e - 4$
43 $[43, 43, -2w^{2} + 3w + 6]$ $\phantom{-}e - 4$
43 $[43, 43, -w^{2} + 6]$ $-2e$
49 $[49, 7, w^{2} + w - 3]$ $-2e^{2} - 2e + 10$
53 $[53, 53, 2w^{2} - 5w - 4]$ $\phantom{-}6$
59 $[59, 59, 2w - 3]$ $\phantom{-}e^{2} + 2e - 8$
61 $[61, 61, -w - 4]$ $-2e^{2} - 4e + 14$
67 $[67, 67, -2w^{2} - w + 2]$ $-2e^{2} - 4e + 12$
73 $[73, 73, 2w^{2} - 3w - 12]$ $\phantom{-}2$
83 $[83, 83, -2w - 5]$ $\phantom{-}2e^{2} - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 1]$ $-1$
$9$ $[9, 3, w^{2} - 2]$ $1$