Properties

Label 4.4.16317.1-9.1-c
Base field 4.4.16317.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - w^{2} - 4w]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.16317.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - w^{2} - 4w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 16x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - 3$
7 $[7, 7, -w^{2} + 2]$ $-\frac{1}{2}e^{2} + 5$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{2}e^{3} + 9e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
25 $[25, 5, w^{2} - w - 3]$ $\phantom{-}4$
37 $[37, 37, 2w - 1]$ $\phantom{-}6$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - 3$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-\frac{1}{2}e^{2} + 5$
59 $[59, 59, 2w - 5]$ $\phantom{-}\frac{1}{2}e^{3} - 11e$
59 $[59, 59, -2w - 3]$ $-\frac{3}{2}e^{3} + 25e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}e^{2} - 6$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $-e^{2} + 10$
83 $[83, 83, -w^{3} + 7w]$ $-\frac{3}{2}e^{3} + 23e$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{1}{2}e^{3} + 9e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
83 $[83, 83, w^{2} - 2w - 6]$ $-\frac{1}{2}e^{3} + 5e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - w^{2} - 4w]$ $1$