Properties

Label 4.4.19796.1-8.4-c
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 8, w]$
Dimension $10$
CM no
Base change no

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Base field 4.4.19796.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 8, w]$
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:

\(x^{10} - 36x^{8} + 400x^{6} - 1648x^{4} + 2048x^{2} - 512\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}0$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $-\frac{1}{176}e^{8} + \frac{31}{176}e^{6} - \frac{16}{11}e^{4} + \frac{79}{22}e^{2} - \frac{13}{11}$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}\frac{9}{704}e^{9} - \frac{39}{88}e^{7} + \frac{199}{44}e^{5} - \frac{669}{44}e^{3} + \frac{98}{11}e$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}\frac{3}{704}e^{9} - \frac{13}{88}e^{7} + \frac{35}{22}e^{5} - \frac{311}{44}e^{3} + \frac{128}{11}e$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}\frac{3}{176}e^{9} - \frac{13}{22}e^{7} + \frac{269}{44}e^{5} - \frac{245}{11}e^{3} + \frac{226}{11}e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{176}e^{8} - \frac{21}{88}e^{6} + \frac{141}{44}e^{4} - \frac{155}{11}e^{2} + \frac{112}{11}$
31 $[31, 31, -w^{2} + w + 1]$ $\phantom{-}\frac{7}{704}e^{9} - \frac{17}{44}e^{7} + \frac{211}{44}e^{5} - \frac{953}{44}e^{3} + \frac{273}{11}e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{5}{704}e^{9} - \frac{9}{44}e^{7} + \frac{29}{22}e^{5} - \frac{27}{44}e^{3} - \frac{47}{11}e$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-e$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $-\frac{1}{176}e^{8} + \frac{21}{88}e^{6} - \frac{141}{44}e^{4} + \frac{166}{11}e^{2} - \frac{134}{11}$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $-\frac{1}{2}e^{3} + 7e$
61 $[61, 61, 2w^{2} - 7]$ $-\frac{7}{704}e^{9} + \frac{17}{44}e^{7} - \frac{211}{44}e^{5} + \frac{953}{44}e^{3} - \frac{240}{11}e$
71 $[71, 71, w^{2} - 3w - 5]$ $\phantom{-}\frac{3}{176}e^{8} - \frac{41}{88}e^{6} + \frac{115}{44}e^{4} - \frac{3}{11}e^{2} - \frac{16}{11}$
73 $[73, 73, 2w - 3]$ $\phantom{-}\frac{15}{704}e^{9} - \frac{65}{88}e^{7} + \frac{339}{44}e^{5} - \frac{1313}{44}e^{3} + \frac{398}{11}e$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}\frac{5}{704}e^{9} - \frac{9}{44}e^{7} + \frac{29}{22}e^{5} - \frac{5}{44}e^{3} - \frac{124}{11}e$
79 $[79, 79, 2w^{2} - 5]$ $\phantom{-}\frac{1}{88}e^{8} - \frac{31}{88}e^{6} + \frac{117}{44}e^{4} - \frac{24}{11}e^{2} - \frac{40}{11}$
81 $[81, 3, -3]$ $-\frac{1}{44}e^{8} + \frac{31}{44}e^{6} - \frac{64}{11}e^{4} + \frac{158}{11}e^{2} - \frac{30}{11}$
101 $[101, 101, 2w^{2} - 4w - 9]$ $-\frac{3}{704}e^{9} + \frac{13}{88}e^{7} - \frac{35}{22}e^{5} + \frac{311}{44}e^{3} - \frac{128}{11}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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