Properties

Label 4.4.14656.1-12.1-c
Base field 4.4.14656.1
Weight $[2, 2, 2, 2]$
Level norm $12$
Level $[12, 6, -w^{2} + 2w]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.14656.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[12, 6, -w^{2} + 2w]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}1$
5 $[5, 5, -w^{2} + w + 1]$ $\phantom{-}2$
11 $[11, 11, w^{2} - 3]$ $\phantom{-}2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}0$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}8$
27 $[27, 3, w^{3} - 3w^{2} - w + 5]$ $\phantom{-}0$
41 $[41, 41, -w^{3} + 2w^{2} + w - 1]$ $\phantom{-}6$
41 $[41, 41, -w^{3} + w^{2} + 2w - 1]$ $-6$
43 $[43, 43, w^{3} - w^{2} - 5w + 1]$ $-6$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}6$
47 $[47, 47, -2w^{3} + 6w^{2} + w - 5]$ $\phantom{-}2$
61 $[61, 61, -2w^{3} + 5w^{2} + 4w - 7]$ $-8$
67 $[67, 67, -2w^{2} + 2w + 9]$ $-2$
67 $[67, 67, -w^{3} + 2w^{2} + 4w - 1]$ $-4$
71 $[71, 71, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}8$
83 $[83, 83, -w^{3} + 2w^{2} + 5w + 1]$ $\phantom{-}12$
89 $[89, 89, -w - 3]$ $-8$
89 $[89, 89, -w^{2} - 2w + 1]$ $\phantom{-}6$
97 $[97, 97, w^{3} - w^{2} - 6w + 1]$ $\phantom{-}16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$3$ $[3, 3, w + 1]$ $-1$