Properties

Label 4.4.17428.1-9.1-k
Base field 4.4.17428.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 9, w^{2} + w - 3]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.17428.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 9, w^{2} + w - 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 9x^{2} + 19\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e^{2} - 3$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}0$
27 $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ $\phantom{-}e^{3} - 4e$
29 $[29, 29, w^{3} + w^{2} - 2w - 1]$ $\phantom{-}5e^{2} - 19$
31 $[31, 31, -w^{2} - w + 1]$ $\phantom{-}e^{3} - 5e$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ $\phantom{-}e^{3} - 8e$
37 $[37, 37, -w^{3} + 3w + 1]$ $-e^{3} + 2e$
41 $[41, 41, -w^{2} + w + 5]$ $-e^{2}$
41 $[41, 41, -w^{3} + w^{2} + 4w - 1]$ $-2e^{3} + 9e$
43 $[43, 43, -2w - 1]$ $\phantom{-}e$
47 $[47, 47, w^{2} + w - 5]$ $-7e^{2} + 29$
47 $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ $\phantom{-}3$
53 $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ $-2e^{3} + 6e$
59 $[59, 59, w^{3} + w^{2} - 4w - 1]$ $-2e^{2} + 9$
59 $[59, 59, w^{3} + w^{2} - 4w - 5]$ $-e^{2} + 13$
71 $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ $-2e^{3} + 12e$
71 $[71, 71, w^{2} + 3w + 1]$ $\phantom{-}6e^{3} - 27e$
73 $[73, 73, w^{3} - 5w + 1]$ $-3e^{3} + 12e$
89 $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ $\phantom{-}2e^{3} - 11e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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