Properties

Label 4.4.16448.2-14.3-d
Base field 4.4.16448.2
Weight $[2, 2, 2, 2]$
Level norm $14$
Level $[14,14,w^{3} - 2w^{2} - 4w + 7]$
Dimension $3$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.16448.2

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[14,14,w^{3} - 2w^{2} - 4w + 7]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $21$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ $\phantom{-}e$
2 $[2, 2, w^{3} - 6w - 5]$ $-1$
7 $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 5w + 3]$ $\phantom{-}e^{2} - e - 4$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ $\phantom{-}0$
31 $[31, 31, -w^{2} - w + 1]$ $-2e^{2} + 2e + 8$
31 $[31, 31, -w^{2} + 3w - 1]$ $\phantom{-}e^{2} + e - 6$
31 $[31, 31, -w^{3} + w^{2} + 4w + 1]$ $-e^{2} - 3e$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ $-4e^{2} + 10$
41 $[41, 41, w^{3} + w^{2} - 8w - 11]$ $\phantom{-}2e^{2} - 2e - 2$
47 $[47, 47, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{2} + e - 6$
47 $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}2e^{2} - 2e - 8$
49 $[49, 7, 2w^{2} - 2w - 9]$ $-3e^{2} + 5e + 8$
71 $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ $-4e - 4$
71 $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ $\phantom{-}3e^{2} - e - 6$
73 $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ $-3e^{2} - e + 2$
73 $[73, 73, w^{3} - 5w - 1]$ $\phantom{-}4e + 2$
73 $[73, 73, w^{3} - 7w - 3]$ $-3e^{2} - 3e + 8$
73 $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ $-4e - 2$
81 $[81, 3, -3]$ $\phantom{-}2e^{2} + 2e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w^{3} + 6w + 5]$ $1$
$7$ $[7,7,w^{3} - 3w^{2} - 2w + 7]$ $-1$