Properties

Label 4.4.5744.1-43.1-c
Base field 4.4.5744.1
Weight $[2, 2, 2, 2]$
Level norm $43$
Level $[43, 43, -w - 3]$
Dimension $10$
CM no
Base change no

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Base field 4.4.5744.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[43, 43, -w - 3]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 36x^{8} + 466x^{6} - 2588x^{4} + 5293x^{2} - 384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{319}{64}e^{5} - \frac{1209}{64}e^{3} + \frac{137}{8}e$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{311}{64}e^{5} - \frac{1049}{64}e^{3} + \frac{27}{4}e$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $-\frac{1}{32}e^{8} + \frac{31}{32}e^{6} - \frac{311}{32}e^{4} + \frac{1033}{32}e^{2} - 8$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + \frac{91}{8}e$
17 $[17, 17, -w^{2} + 2]$ $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{315}{32}e^{5} - \frac{1145}{32}e^{3} + \frac{227}{8}e$
19 $[19, 19, -w^{3} + 5w]$ $-\frac{1}{2}e^{3} + \frac{11}{2}e$
31 $[31, 31, -w^{2} + 2w + 3]$ $-\frac{7}{64}e^{8} + \frac{201}{64}e^{6} - \frac{1809}{64}e^{4} + \frac{5119}{64}e^{2} - 2$
37 $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ $-\frac{1}{64}e^{9} + \frac{31}{64}e^{7} - \frac{319}{64}e^{5} + \frac{1209}{64}e^{3} - \frac{137}{8}e$
43 $[43, 43, -w - 3]$ $-1$
53 $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{335}{64}e^{5} - \frac{1561}{64}e^{3} + \frac{363}{8}e$
53 $[53, 53, w^{3} - 6w - 2]$ $\phantom{-}\frac{5}{32}e^{8} - \frac{151}{32}e^{6} + \frac{1443}{32}e^{4} - \frac{4353}{32}e^{2} + 6$
59 $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ $-\frac{3}{32}e^{8} + \frac{89}{32}e^{6} - \frac{837}{32}e^{4} + \frac{2559}{32}e^{2} - 12$
61 $[61, 61, 2w^{3} - w^{2} - 10w]$ $\phantom{-}\frac{1}{16}e^{8} - \frac{27}{16}e^{6} + \frac{223}{16}e^{4} - \frac{549}{16}e^{2} - 8$
61 $[61, 61, 2w^{3} - w^{2} - 8w]$ $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{307}{32}e^{5} - \frac{985}{32}e^{3} + \frac{37}{8}e$
71 $[71, 71, 2w^{3} - 9w - 2]$ $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + \frac{91}{4}e$
73 $[73, 73, -w^{3} - w^{2} + 6w + 3]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + \frac{99}{8}e$
81 $[81, 3, -3]$ $\phantom{-}\frac{5}{64}e^{8} - \frac{139}{64}e^{6} + \frac{1187}{64}e^{4} - \frac{3117}{64}e^{2} - 2$
83 $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{311}{32}e^{5} - \frac{1033}{32}e^{3} + 8e$
101 $[101, 101, 2w^{3} - 8w - 3]$ $\phantom{-}\frac{3}{8}e^{5} - 8e^{3} + \frac{293}{8}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43, 43, -w - 3]$ $1$