Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 4
Level $[4, 2, w^{2} - 2w - 3]$
Label 3.3.940.1-4.2-a
Dimension 2
CM no
Base change no

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Base field 3.3.940.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 4\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[4, 2, w^{2} - 2w - 3]$
Label 3.3.940.1-4.2-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
5 $[5, 5, -w^{2} + w + 7]$ $\phantom{-}e - 2$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}2e - 3$
17 $[17, 17, -w^{2} + 3w + 1]$ $-2e - 1$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}4e - 2$
27 $[27, 3, 3]$ $-2e - 2$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}e - 2$
37 $[37, 37, w^{2} + w + 1]$ $\phantom{-}e - 8$
41 $[41, 41, w^{2} - w - 9]$ $\phantom{-}3e + 4$
43 $[43, 43, -3w^{2} + 3w + 17]$ $-6e + 4$
47 $[47, 47, 2w^{2} - 2w - 13]$ $\phantom{-}2e - 8$
47 $[47, 47, -2w + 5]$ $\phantom{-}2e - 2$
53 $[53, 53, 3w^{2} - w - 19]$ $-2e - 7$
59 $[59, 59, 2w - 1]$ $\phantom{-}14$
67 $[67, 67, w^{2} + w - 5]$ $\phantom{-}10e - 10$
71 $[71, 71, -3w^{2} + w + 21]$ $-4e + 10$
79 $[79, 79, 3w^{2} - w - 23]$ $\phantom{-}8e - 10$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-1$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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