Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 10
Level $[10, 10, -w - 3]$
Label 3.3.940.1-10.1-b
Dimension 4
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 $[10, 10, -w - 3]$
Label 3.3.940.1-10.1-b
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 8x^{2} + 2x + 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}1$
5 $[5, 5, -w^{2} + w + 7]$ $-1$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}e^{3} + 2e^{2} - 5e - 6$
17 $[17, 17, -w^{2} + 3w + 1]$ $-2e + 2$
23 $[23, 23, -w^{2} + w + 3]$ $-2e^{2} + 10$
27 $[27, 3, 3]$ $\phantom{-}2e^{2} + 2e - 8$
29 $[29, 29, -w^{2} + 3w - 1]$ $-2e^{3} + 10e - 2$
37 $[37, 37, w^{2} + w + 1]$ $\phantom{-}2e^{3} + 2e^{2} - 12e - 6$
41 $[41, 41, w^{2} - w - 9]$ $-2$
43 $[43, 43, -3w^{2} + 3w + 17]$ $\phantom{-}e^{3} - 3e$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{3} - 4e^{2} + 3e + 20$
47 $[47, 47, -2w + 5]$ $-3e^{3} - 2e^{2} + 13e + 2$
53 $[53, 53, 3w^{2} - w - 19]$ $-e^{3} - 2e^{2} + 7e + 4$
59 $[59, 59, 2w - 1]$ $-2e^{3} - 8e^{2} + 8e + 28$
67 $[67, 67, w^{2} + w - 5]$ $\phantom{-}e^{3} - 5e + 6$
71 $[71, 71, -3w^{2} + w + 21]$ $-2e^{3} - 6e^{2} + 8e + 24$
79 $[79, 79, 3w^{2} - w - 23]$ $\phantom{-}2e^{3} + 2e^{2} - 8e$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-2e^{2} + 20$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-4e^{3} - 6e^{2} + 14e + 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $-1$
5 $[5, 5, -w^{2} + w + 7]$ $1$