Properties

Label 4.4.17609.1-16.1-c
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $9$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 4x^{8} - 23x^{7} + 84x^{6} + 188x^{5} - 580x^{4} - 636x^{3} + 1522x^{2} + 764x - 1176\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $-1$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 6w - 2]$ $-\frac{149}{6304}e^{8} + \frac{609}{6304}e^{7} + \frac{1285}{3152}e^{6} - \frac{4847}{3152}e^{5} - \frac{6031}{3152}e^{4} + \frac{20001}{3152}e^{3} + \frac{557}{3152}e^{2} - \frac{9809}{1576}e + \frac{5671}{788}$
8 $[8, 2, w^{3} - 7w + 3]$ $-1$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}\frac{383}{12608}e^{8} - \frac{275}{12608}e^{7} - \frac{5831}{6304}e^{6} + \frac{253}{6304}e^{5} + \frac{57917}{6304}e^{4} + \frac{22861}{6304}e^{3} - \frac{197575}{6304}e^{2} - \frac{47589}{3152}e + \frac{41355}{1576}$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}\frac{247}{12608}e^{8} - \frac{523}{12608}e^{7} - \frac{3135}{6304}e^{6} + \frac{3381}{6304}e^{5} + \frac{28677}{6304}e^{4} - \frac{7115}{6304}e^{3} - \frac{100095}{6304}e^{2} - \frac{1837}{3152}e + \frac{23547}{1576}$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{247}{12608}e^{8} + \frac{523}{12608}e^{7} + \frac{3135}{6304}e^{6} - \frac{3381}{6304}e^{5} - \frac{28677}{6304}e^{4} + \frac{7115}{6304}e^{3} + \frac{100095}{6304}e^{2} + \frac{1837}{3152}e - \frac{23547}{1576}$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $\phantom{-}\frac{585}{12608}e^{8} - \frac{741}{12608}e^{7} - \frac{9001}{6304}e^{6} + \frac{5851}{6304}e^{5} + \frac{90315}{6304}e^{4} - \frac{17349}{6304}e^{3} - \frac{306577}{6304}e^{2} - \frac{5595}{3152}e + \frac{57677}{1576}$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $-\frac{149}{6304}e^{8} + \frac{609}{6304}e^{7} + \frac{1285}{3152}e^{6} - \frac{4847}{3152}e^{5} - \frac{6031}{3152}e^{4} + \frac{20001}{3152}e^{3} - \frac{2595}{3152}e^{2} - \frac{9809}{1576}e + \frac{10399}{788}$
41 $[41, 41, w^{2} + 2w - 4]$ $-\frac{111}{12608}e^{8} + \frac{771}{12608}e^{7} + \frac{439}{6304}e^{6} - \frac{6509}{6304}e^{5} + \frac{563}{6304}e^{4} + \frac{37091}{6304}e^{3} + \frac{2615}{6304}e^{2} - \frac{40763}{3152}e - \frac{5739}{1576}$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-\frac{883}{12608}e^{8} + \frac{1959}{12608}e^{7} + \frac{11571}{6304}e^{6} - \frac{15545}{6304}e^{5} - \frac{102377}{6304}e^{4} + \frac{57351}{6304}e^{3} + \frac{313995}{6304}e^{2} - \frac{17175}{3152}e - \frac{55791}{1576}$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}\frac{209}{6304}e^{8} - \frac{685}{6304}e^{7} - \frac{2289}{3152}e^{6} + \frac{5043}{3152}e^{5} + \frac{18931}{3152}e^{4} - \frac{14749}{3152}e^{3} - \frac{67481}{3152}e^{2} - \frac{3979}{1576}e + \frac{19197}{788}$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}\frac{159}{3152}e^{8} - \frac{359}{3152}e^{7} - \frac{2109}{1576}e^{6} + \frac{3041}{1576}e^{5} + \frac{18425}{1576}e^{4} - \frac{12559}{1576}e^{3} - \frac{53475}{1576}e^{2} + \frac{5541}{788}e + \frac{8061}{394}$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-\frac{193}{3152}e^{8} + \frac{297}{3152}e^{7} + \frac{2783}{1576}e^{6} - \frac{2259}{1576}e^{5} - \frac{25735}{1576}e^{4} + \frac{5065}{1576}e^{3} + \frac{76269}{1576}e^{2} + \frac{5897}{788}e - \frac{10149}{394}$
59 $[59, 59, w^{2} + w - 1]$ $\phantom{-}\frac{383}{12608}e^{8} - \frac{275}{12608}e^{7} - \frac{5831}{6304}e^{6} + \frac{253}{6304}e^{5} + \frac{57917}{6304}e^{4} + \frac{22861}{6304}e^{3} - \frac{210183}{6304}e^{2} - \frac{41285}{3152}e + \frac{60267}{1576}$
59 $[59, 59, w^{2} + 2w - 6]$ $\phantom{-}\frac{639}{12608}e^{8} - \frac{179}{12608}e^{7} - \frac{10535}{6304}e^{6} - \frac{2483}{6304}e^{5} + \frac{112957}{6304}e^{4} + \frac{57037}{6304}e^{3} - \frac{409991}{6304}e^{2} - \frac{98853}{3152}e + \frac{86835}{1576}$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-\frac{37}{394}e^{8} + \frac{30}{197}e^{7} + \frac{1015}{394}e^{6} - \frac{331}{197}e^{5} - \frac{4803}{197}e^{4} - \frac{310}{197}e^{3} + \frac{16172}{197}e^{2} + \frac{4870}{197}e - \frac{13562}{197}$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}\frac{1383}{12608}e^{8} - \frac{3643}{12608}e^{7} - \frac{17311}{6304}e^{6} + \frac{30837}{6304}e^{5} + \frac{146837}{6304}e^{4} - \frac{131259}{6304}e^{3} - \frac{430415}{6304}e^{2} + \frac{47267}{3152}e + \frac{73379}{1576}$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-\frac{1545}{12608}e^{8} + \frac{5109}{12608}e^{7} + \frac{17185}{6304}e^{6} - \frac{43659}{6304}e^{5} - \frac{129659}{6304}e^{4} + \frac{201237}{6304}e^{3} + \frac{340353}{6304}e^{2} - \frac{112637}{3152}e - \frac{50533}{1576}$
81 $[81, 3, -3]$ $\phantom{-}\frac{117}{12608}e^{8} - \frac{1409}{12608}e^{7} + \frac{91}{6304}e^{6} + \frac{15039}{6304}e^{5} - \frac{13457}{6304}e^{4} - \frac{96769}{6304}e^{3} + \frac{68547}{6304}e^{2} + \frac{87137}{3152}e - \frac{11159}{1576}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $1$
$8$ $[8, 2, w^{3} - 7w + 3]$ $1$