Properties

Label 4.4.6809.1-22.1-f
Base field 4.4.6809.1
Weight $[2, 2, 2, 2]$
Level norm $22$
Level $[22, 22, -w^{2} + 3]$
Dimension $3$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.6809.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[22, 22, -w^{2} + 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 15x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$
11 $[11, 11, w^{3} - 5w + 1]$ $\phantom{-}1$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 7$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 5$
29 $[29, 29, -w^{2} - w + 3]$ $-2e + 2$
31 $[31, 31, -w^{3} + 6w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 9$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}e - 2$
47 $[47, 47, 2w^{3} - 9w]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 9$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $\phantom{-}e + 2$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $-e^{2} + e + 4$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}e^{2} - e - 10$
59 $[59, 59, 3w^{3} - 15w - 5]$ $\phantom{-}e^{2} - e - 10$
71 $[71, 71, w^{3} - 3w - 3]$ $-2e + 4$
81 $[81, 3, -3]$ $\phantom{-}e - 4$
83 $[83, 83, -2w^{3} + 8w + 3]$ $-e^{2} - e + 6$
89 $[89, 89, -2w^{3} + 11w - 2]$ $-e^{2} - e + 12$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-2e - 6$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $\phantom{-}2e + 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 1]$ $-1$
$11$ $[11, 11, w^{3} - 5w + 1]$ $-1$