Properties

Label 6.6.966125.1-31.2-c
Base field 6.6.966125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, -w^{2} + 2]$
Dimension $7$
CM no
Base change no

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Base field 6.6.966125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[31, 31, -w^{2} + 2]$
Dimension: $7$
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:

\(x^{7} - 6x^{6} - x^{5} + 43x^{4} - 16x^{3} - 53x^{2} + 25x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $-e + 2$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ $-\frac{1}{3}e^{6} + 2e^{5} - \frac{40}{3}e^{3} + \frac{19}{3}e^{2} + \frac{49}{3}e - 2$
25 $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ $\phantom{-}\frac{1}{3}e^{6} - \frac{7}{3}e^{5} + e^{4} + \frac{46}{3}e^{3} - \frac{32}{3}e^{2} - 15e + \frac{28}{3}$
29 $[29, 29, -w^{4} + 4w^{2} + 1]$ $-e^{6} + \frac{16}{3}e^{5} + 4e^{4} - 40e^{3} - \frac{8}{3}e^{2} + \frac{152}{3}e - \frac{22}{3}$
31 $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ $-\frac{1}{3}e^{6} + \frac{5}{3}e^{5} + e^{4} - \frac{37}{3}e^{3} + 6e^{2} + \frac{62}{3}e - \frac{20}{3}$
31 $[31, 31, -w^{2} + 2]$ $-1$
59 $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ $\phantom{-}\frac{2}{3}e^{6} - \frac{10}{3}e^{5} - 2e^{4} + \frac{62}{3}e^{3} - 3e^{2} - \frac{46}{3}e + \frac{28}{3}$
59 $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ $-\frac{1}{3}e^{6} + 2e^{5} - \frac{40}{3}e^{3} + \frac{22}{3}e^{2} + \frac{46}{3}e - 8$
59 $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ $\phantom{-}e^{6} - 6e^{5} - 2e^{4} + 45e^{3} - 8e^{2} - 53e + 18$
61 $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ $\phantom{-}\frac{1}{3}e^{6} - \frac{5}{3}e^{5} - e^{4} + \frac{34}{3}e^{3} - 3e^{2} - \frac{50}{3}e + \frac{26}{3}$
64 $[64, 2, 2]$ $-\frac{1}{3}e^{6} + 2e^{5} + e^{4} - \frac{46}{3}e^{3} - \frac{8}{3}e^{2} + \frac{64}{3}e + 1$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ $\phantom{-}2e^{6} - \frac{35}{3}e^{5} - 5e^{4} + 87e^{3} - \frac{26}{3}e^{2} - \frac{322}{3}e + \frac{68}{3}$
71 $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ $\phantom{-}\frac{1}{3}e^{6} - 2e^{5} + \frac{43}{3}e^{3} - \frac{25}{3}e^{2} - \frac{70}{3}e + 8$
71 $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ $-\frac{2}{3}e^{5} + 2e^{4} + 6e^{3} - \frac{35}{3}e^{2} - \frac{43}{3}e + \frac{38}{3}$
71 $[71, 71, w^{3} - 5w]$ $-e^{6} + \frac{17}{3}e^{5} + 2e^{4} - 41e^{3} + \frac{38}{3}e^{2} + \frac{160}{3}e - \frac{56}{3}$
79 $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ $\phantom{-}\frac{2}{3}e^{5} - 2e^{4} - 6e^{3} + \frac{41}{3}e^{2} + \frac{28}{3}e - \frac{44}{3}$
89 $[89, 89, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{4}{3}e^{6} - 7e^{5} - 5e^{4} + \frac{148}{3}e^{3} + \frac{14}{3}e^{2} - \frac{169}{3}e + 4$
101 $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ $\phantom{-}\frac{5}{3}e^{6} - \frac{29}{3}e^{5} - 4e^{4} + \frac{218}{3}e^{3} - \frac{31}{3}e^{2} - 98e + \frac{50}{3}$
101 $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ $-\frac{1}{3}e^{6} + \frac{8}{3}e^{5} - 2e^{4} - \frac{61}{3}e^{3} + 21e^{2} + \frac{107}{3}e - \frac{68}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -w^{2} + 2]$ $1$