Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 9
Level $[9, 3, w^{2} - 7]$
Label 3.3.1129.1-9.3-b
Dimension 3
CM no
Base change no

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Base field 3.3.1129.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[9, 3, w^{2} - 7]$
Label 3.3.1129.1-9.3-b
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 4x^{2} + x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
8 $[8, 2, 2]$ $-e^{2} + 3e + 1$
11 $[11, 11, -w^{2} + 5]$ $-e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}2e - 2$
17 $[17, 17, -w^{2} + w + 4]$ $-2e^{2} + 4e + 2$
19 $[19, 19, -w^{2} - w + 4]$ $-2e^{2} + 3e + 8$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-e^{2} + 6e - 2$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}3e^{2} - 10e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-e^{2} + 6$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}4e - 6$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}2e^{2} - 4e + 4$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}2e^{2} - 4e - 2$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}4e^{2} - 8e - 4$
73 $[73, 73, -w^{2} - 1]$ $\phantom{-}2e^{2} - 7e - 2$
83 $[83, 83, w^{2} - w - 10]$ $-5e^{2} + 10e + 12$
89 $[89, 89, -w^{2} + 4w - 2]$ $-2e^{2} + 5e - 2$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}4e^{2} - 10e - 6$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}2e^{2} - 12e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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