Properties

Label 4.4.3981.1-39.1-e
Base field 4.4.3981.1
Weight $[2, 2, 2, 2]$
Level norm $39$
Level $[39, 39, -w^{2} - w + 3]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.3981.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[39, 39, -w^{2} - w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} - w^{2} - 3w + 1]$ $-2$
9 $[9, 3, -w^{2} + 2]$ $-2$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $-1$
16 $[16, 2, 2]$ $-5$
23 $[23, 23, w^{2} - 2w - 2]$ $\phantom{-}0$
37 $[37, 37, w^{3} - 4w + 1]$ $-6$
37 $[37, 37, w^{3} - w^{2} - 5w + 1]$ $-2$
41 $[41, 41, w^{3} - 5w + 1]$ $\phantom{-}2$
43 $[43, 43, 2w^{3} - w^{2} - 7w]$ $\phantom{-}0$
53 $[53, 53, 2w - 3]$ $-2$
59 $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ $-4$
67 $[67, 67, -w - 3]$ $-8$
67 $[67, 67, w^{3} + w^{2} - 5w - 4]$ $-12$
71 $[71, 71, 2w^{3} - 3w^{2} - 7w + 5]$ $\phantom{-}8$
73 $[73, 73, w^{3} - 6w]$ $-2$
73 $[73, 73, -w^{3} - w^{2} + 5w + 3]$ $-6$
79 $[79, 79, w^{3} - 3w - 4]$ $\phantom{-}16$
83 $[83, 83, w^{3} - 2w^{2} - 3w + 1]$ $-16$
83 $[83, 83, -2w^{3} + 2w^{2} + 6w - 3]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$
$13$ $[13, 13, -w^{3} + w^{2} + 4w]$ $1$