Properties

Label 4.4.16448.1-22.1-c
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $22$
Level $[22, 22, -w + 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.16448.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[22, 22, -w + 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 17x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-\frac{1}{5}e^{2} - \frac{3}{5}e + \frac{18}{5}$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $\phantom{-}1$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}2$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $\phantom{-}\frac{2}{5}e^{2} - \frac{4}{5}e - \frac{21}{5}$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{2}{5}e^{2} - \frac{6}{5}e + \frac{36}{5}$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}4$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}0$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{5}e^{2} - \frac{2}{5}e - \frac{18}{5}$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $-\frac{1}{5}e^{2} - \frac{8}{5}e + \frac{18}{5}$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $-\frac{2}{5}e^{2} + \frac{4}{5}e + \frac{36}{5}$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $-\frac{1}{5}e^{2} - \frac{3}{5}e + \frac{28}{5}$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $\phantom{-}\frac{4}{5}e^{2} + \frac{2}{5}e - \frac{52}{5}$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $\phantom{-}\frac{4}{5}e^{2} - \frac{8}{5}e - \frac{52}{5}$
81 $[81, 3, -3]$ $\phantom{-}\frac{2}{5}e^{2} + \frac{6}{5}e - \frac{21}{5}$
83 $[83, 83, -w - 3]$ $\phantom{-}\frac{3}{5}e^{2} - \frac{11}{5}e - \frac{44}{5}$
83 $[83, 83, w^{2} - 3w - 7]$ $\phantom{-}e^{2} - 4$
89 $[89, 89, w^{2} - 2w - 7]$ $\phantom{-}e + 10$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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