Properties

Label 4.4.14197.1-31.2-b
Base field 4.4.14197.1
Weight $[2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{2} - 2]$
Dimension $1$
CM no
Base change no

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Base field 4.4.14197.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[31, 31, w^{2} - 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w - 1]$ $-2$
9 $[9, 3, w^{3} - 5w - 2]$ $-4$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-2$
13 $[13, 13, -w + 2]$ $-2$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, w^{3} - w^{2} - 5w]$ $\phantom{-}4$
19 $[19, 19, -w^{3} + w^{2} + 6w]$ $\phantom{-}4$
23 $[23, 23, -w^{2} + w + 3]$ $-8$
29 $[29, 29, w^{3} - 5w]$ $\phantom{-}4$
31 $[31, 31, w^{3} - 6w - 1]$ $\phantom{-}4$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}1$
37 $[37, 37, -w - 3]$ $\phantom{-}4$
37 $[37, 37, w^{3} - 4w - 1]$ $-12$
37 $[37, 37, w^{3} - 7w - 4]$ $-2$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}10$
43 $[43, 43, w^{2} + w - 3]$ $\phantom{-}8$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}8$
47 $[47, 47, -w^{3} + w^{2} + 5w - 4]$ $\phantom{-}12$
53 $[53, 53, w^{3} - 6w]$ $-10$
61 $[61, 61, w^{3} - w^{2} - 7w - 2]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{2} - 2]$ $-1$