Properties

Label 6.6.820125.1-64.1-f
Base field 6.6.820125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $64$
Level $[64, 2, 2]$
Dimension $9$
CM no
Base change yes

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Base field 6.6.820125.1

Generator \(w\), with minimal polynomial \(x^{6} - 9x^{4} - 4x^{3} + 9x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[64, 2, 2]$
Dimension: $9$
CM: no
Base change: yes
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 7x^{8} - 75x^{7} + 470x^{6} + 1562x^{5} - 7523x^{4} - 5793x^{3} + 9763x^{2} + 2400x - 2131\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -\frac{6}{19}w^{5} + \frac{4}{19}w^{4} + \frac{45}{19}w^{3} - \frac{6}{19}w^{2} - \frac{12}{19}w + \frac{28}{19}]$ $...$
19 $[19, 19, -\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{18}{19}w^{2} - \frac{116}{19}w + \frac{11}{19}]$ $\phantom{-}e$
19 $[19, 19, -\frac{10}{19}w^{5} - \frac{6}{19}w^{4} + \frac{94}{19}w^{3} + \frac{85}{19}w^{2} - \frac{77}{19}w - \frac{42}{19}]$ $\phantom{-}e$
19 $[19, 19, -\frac{16}{19}w^{5} - \frac{2}{19}w^{4} + \frac{139}{19}w^{3} + \frac{79}{19}w^{2} - \frac{108}{19}w - \frac{33}{19}]$ $...$
19 $[19, 19, -\frac{4}{19}w^{5} + \frac{9}{19}w^{4} + \frac{30}{19}w^{3} - \frac{61}{19}w^{2} - \frac{8}{19}w + \frac{44}{19}]$ $...$
19 $[19, 19, -\frac{8}{19}w^{5} - \frac{1}{19}w^{4} + \frac{79}{19}w^{3} + \frac{30}{19}w^{2} - \frac{111}{19}w - \frac{7}{19}]$ $...$
19 $[19, 19, \frac{2}{19}w^{5} + \frac{5}{19}w^{4} - \frac{15}{19}w^{3} - \frac{55}{19}w^{2} - \frac{34}{19}w + \frac{35}{19}]$ $...$
64 $[64, 2, 2]$ $-1$
71 $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ $...$
71 $[71, 71, -\frac{11}{19}w^{5} + \frac{20}{19}w^{4} + \frac{92}{19}w^{3} - \frac{125}{19}w^{2} - \frac{117}{19}w + \frac{64}{19}]$ $...$
71 $[71, 71, \frac{12}{19}w^{5} - \frac{8}{19}w^{4} - \frac{109}{19}w^{3} + \frac{12}{19}w^{2} + \frac{138}{19}w + \frac{1}{19}]$ $...$
71 $[71, 71, \frac{22}{19}w^{5} - \frac{21}{19}w^{4} - \frac{184}{19}w^{3} + \frac{79}{19}w^{2} + \frac{177}{19}w - \frac{52}{19}]$ $...$
71 $[71, 71, w^{5} - w^{4} - 8w^{3} + 4w^{2} + 6w - 3]$ $...$
71 $[71, 71, -\frac{24}{19}w^{5} + \frac{16}{19}w^{4} + \frac{199}{19}w^{3} - \frac{24}{19}w^{2} - \frac{162}{19}w - \frac{21}{19}]$ $...$
89 $[89, 89, \frac{13}{19}w^{5} + \frac{4}{19}w^{4} - \frac{126}{19}w^{3} - \frac{82}{19}w^{2} + \frac{159}{19}w + \frac{66}{19}]$ $...$
89 $[89, 89, -\frac{17}{19}w^{5} + \frac{5}{19}w^{4} + \frac{137}{19}w^{3} + \frac{40}{19}w^{2} - \frac{53}{19}w - \frac{41}{19}]$ $...$
89 $[89, 89, -\frac{29}{19}w^{5} + \frac{13}{19}w^{4} + \frac{246}{19}w^{3} + \frac{9}{19}w^{2} - \frac{210}{19}w + \frac{15}{19}]$ $...$
89 $[89, 89, \frac{3}{19}w^{5} + \frac{17}{19}w^{4} - \frac{32}{19}w^{3} - \frac{149}{19}w^{2} - \frac{13}{19}w + \frac{62}{19}]$ $...$
89 $[89, 89, \frac{7}{19}w^{5} - \frac{11}{19}w^{4} - \frac{62}{19}w^{3} + \frac{64}{19}w^{2} + \frac{71}{19}w - \frac{39}{19}]$ $...$
89 $[89, 89, -\frac{9}{19}w^{5} + \frac{6}{19}w^{4} + \frac{77}{19}w^{3} - \frac{28}{19}w^{2} - \frac{56}{19}w + \frac{42}{19}]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$64$ $[64, 2, 2]$ $1$