Properties

Label 6.6.592661.1-47.1-d
Base field 6.6.592661.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $47$
Level $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$
Dimension $5$
CM no
Base change no

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Base field 6.6.592661.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$
Dimension: $5$
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:

\(x^{5} - x^{4} - 23x^{3} + 28x^{2} + 80x - 48\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{5} - 5w^{3} + 4w]$ $\phantom{-}e$
13 $[13, 13, -w^{3} + 3w]$ $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - \frac{19}{10}e^{2} + 2e + \frac{16}{5}$
25 $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{10}e^{4} + \frac{1}{10}e^{3} - \frac{23}{10}e^{2} - \frac{7}{5}e + \frac{48}{5}$
31 $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ $\phantom{-}e + 2$
31 $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{2}{5}e^{2} - \frac{17}{5}e + \frac{32}{5}$
37 $[37, 37, w^{4} - 5w^{2} + w + 3]$ $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - \frac{19}{10}e^{2} + 4e + \frac{26}{5}$
43 $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ $-\frac{1}{10}e^{4} - \frac{1}{10}e^{3} + \frac{23}{10}e^{2} + \frac{7}{5}e - \frac{38}{5}$
47 $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ $-1$
49 $[49, 7, -w^{4} + 4w^{2} + w - 3]$ $\phantom{-}\frac{1}{20}e^{4} + \frac{1}{20}e^{3} - \frac{33}{20}e^{2} + \frac{3}{10}e + \frac{54}{5}$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $-\frac{3}{20}e^{4} + \frac{1}{20}e^{3} + \frac{51}{20}e^{2} - \frac{23}{10}e$
59 $[59, 59, w^{4} - 5w^{2} - w + 5]$ $\phantom{-}\frac{3}{20}e^{4} - \frac{1}{20}e^{3} - \frac{71}{20}e^{2} + \frac{23}{10}e + 8$
61 $[61, 61, w^{3} - w^{2} - 3w]$ $\phantom{-}\frac{1}{20}e^{4} + \frac{1}{4}e^{3} - \frac{21}{20}e^{2} - \frac{41}{10}e + \frac{26}{5}$
64 $[64, 2, -2]$ $-\frac{3}{20}e^{4} - \frac{9}{20}e^{3} + \frac{41}{20}e^{2} + \frac{26}{5}e + 1$
67 $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ $-\frac{1}{20}e^{4} - \frac{1}{20}e^{3} + \frac{33}{20}e^{2} + \frac{7}{10}e - \frac{14}{5}$
67 $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{1}{5}e^{2} - \frac{24}{5}e - \frac{16}{5}$
73 $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ $\phantom{-}\frac{3}{10}e^{4} + \frac{1}{2}e^{3} - \frac{53}{10}e^{2} - \frac{28}{5}e + \frac{66}{5}$
73 $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ $\phantom{-}e - 2$
83 $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ $-\frac{3}{20}e^{4} - \frac{1}{20}e^{3} + \frac{9}{4}e^{2} + \frac{2}{5}e + \frac{4}{5}$
97 $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ $\phantom{-}\frac{1}{20}e^{4} - \frac{1}{20}e^{3} + \frac{1}{20}e^{2} + e - \frac{42}{5}$
101 $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ $\phantom{-}\frac{1}{5}e^{4} + \frac{2}{5}e^{3} - 4e^{2} - \frac{21}{5}e + \frac{78}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ $1$