Properties

Label 6.6.1387029.1-25.1-f
Base field 6.6.1387029.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$
Dimension $8$
CM no
Base change no

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Base field 6.6.1387029.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - x^{2} - 4x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 222x^{6} + 14289x^{4} - 241296x^{2} + 506944\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ $\phantom{-}\frac{15203}{1665322432}e^{7} - \frac{1756241}{832661216}e^{5} + \frac{227131043}{1665322432}e^{3} - \frac{380951027}{208165304}e$
7 $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ $\phantom{-}\frac{5799}{1665322432}e^{7} - \frac{532973}{832661216}e^{5} + \frac{28087751}{1665322432}e^{3} + \frac{168684585}{208165304}e$
25 $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ $-1$
37 $[37, 37, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{2351}{208165304}e^{7} - \frac{305817}{104082652}e^{5} + \frac{49760823}{208165304}e^{3} - \frac{163429566}{26020663}e$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}e$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ $\phantom{-}\frac{19905}{832661216}e^{7} - \frac{2367875}{416330608}e^{5} + \frac{326652689}{832661216}e^{3} - \frac{759851485}{104082652}e$
49 $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ $\phantom{-}\frac{10501}{832661216}e^{7} - \frac{1144607}{416330608}e^{5} + \frac{127609397}{832661216}e^{3} - \frac{2050569}{104082652}e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ $-\frac{2637}{52041326}e^{7} + \frac{1117517}{104082652}e^{5} - \frac{67611401}{104082652}e^{3} + \frac{256515119}{26020663}e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}\frac{8197}{208165304}e^{7} - \frac{202925}{26020663}e^{5} + \frac{85461979}{208165304}e^{3} - \frac{119106216}{26020663}e$
61 $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ $\phantom{-}2$
61 $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ $\phantom{-}\frac{45609}{1665322432}e^{7} - \frac{5268723}{832661216}e^{5} + \frac{681393129}{1665322432}e^{3} - \frac{1351018385}{208165304}e$
61 $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ $\phantom{-}\frac{26801}{1665322432}e^{7} - \frac{2822187}{832661216}e^{5} + \frac{283306545}{1665322432}e^{3} + \frac{164583447}{208165304}e$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}2$
64 $[64, 2, -2]$ $-7$
67 $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ $\phantom{-}\frac{14043}{416330608}e^{7} - \frac{1317583}{208165304}e^{5} + \frac{121163135}{416330608}e^{3} - \frac{48762203}{52041326}e$
67 $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ $-\frac{18745}{416330608}e^{7} + \frac{1929217}{208165304}e^{5} - \frac{220684781}{416330608}e^{3} + \frac{323580009}{52041326}e$
71 $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ $\phantom{-}\frac{28}{292367}e^{6} - \frac{5046}{292367}e^{4} + \frac{231008}{292367}e^{2} - \frac{1447192}{292367}$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $\phantom{-}\frac{28}{292367}e^{6} - \frac{5046}{292367}e^{4} + \frac{231008}{292367}e^{2} - \frac{1447192}{292367}$
81 $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ $-\frac{70}{292367}e^{6} + \frac{12615}{292367}e^{4} - \frac{577520}{292367}e^{2} + \frac{4202714}{292367}$
101 $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ $\phantom{-}\frac{132187}{1665322432}e^{7} - \frac{14051537}{832661216}e^{5} + \frac{1620307755}{1665322432}e^{3} - \frac{2307969251}{208165304}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ $1$