Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 11
Level $[11, 11, -w^{2} + 5]$
Label 3.3.1129.1-11.1-b
Dimension 4
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 $[11, 11, -w^{2} + 5]$
Label 3.3.1129.1-11.1-b
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 3x^{3} - 3x^{2} + 11x - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-e^{3} + 2e^{2} + 5e - 6$
3 $[3, 3, w + 2]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-e + 2$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}1$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}2e^{3} - 4e^{2} - 10e + 12$
17 $[17, 17, -w^{2} + w + 4]$ $-2e^{3} + 4e^{2} + 9e - 9$
19 $[19, 19, -w^{2} - w + 4]$ $-3e^{3} + 5e^{2} + 15e - 16$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 7$
31 $[31, 31, w^{2} - 2w - 4]$ $-e^{3} + 3e + 7$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}2e^{3} - 4e^{2} - 7e + 13$
41 $[41, 41, w^{2} - 2]$ $-e^{3} + 3e^{2} + 6e - 10$
59 $[59, 59, 2w^{2} - 13]$ $-5e^{3} + 10e^{2} + 24e - 30$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}4e^{3} - 9e^{2} - 21e + 23$
67 $[67, 67, 2w^{2} - w - 11]$ $-e^{3} + 2e^{2} + 5e + 3$
73 $[73, 73, -w^{2} - 1]$ $-2e^{2} + 3e + 6$
83 $[83, 83, w^{2} - w - 10]$ $\phantom{-}5e^{3} - 10e^{2} - 21e + 30$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}4e^{3} - 9e^{2} - 22e + 33$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}e^{3} + e^{2} - 9e - 1$
97 $[97, 97, -w^{2} - 4w - 5]$ $-5e^{3} + 7e^{2} + 23e - 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{2} + 5]$ $-1$