Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 3
Level $[3, 3, w]$
Label 3.3.1129.1-3.1-a
Dimension 2
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 $[3, 3, w]$
Label 3.3.1129.1-3.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-2e + 1$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}2e - 4$
13 $[13, 13, w^{2} - w - 7]$ $-2e$
17 $[17, 17, -w^{2} + w + 4]$ $-e$
19 $[19, 19, -w^{2} - w + 4]$ $-4e + 4$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}e - 4$
31 $[31, 31, w^{2} - 2w - 4]$ $-e + 8$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-5e + 8$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}4e - 4$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}2e + 2$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}2e + 4$
67 $[67, 67, 2w^{2} - w - 11]$ $-2e + 12$
73 $[73, 73, -w^{2} - 1]$ $\phantom{-}4e + 2$
83 $[83, 83, w^{2} - w - 10]$ $-4$
89 $[89, 89, -w^{2} + 4w - 2]$ $-6e$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}4e - 16$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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