Properties

Label 4.4.11324.1-17.1-d
Base field 4.4.11324.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{3} + w^{2} + 3w - 1]$
Dimension $12$
CM no
Base change no

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Base field 4.4.11324.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{3} + w^{2} + 3w - 1]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 2x^{11} - 19x^{10} + 36x^{9} + 134x^{8} - 235x^{7} - 435x^{6} + 669x^{5} + 677x^{4} - 784x^{3} - 552x^{2} + 320x + 200\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}\frac{9}{50}e^{11} - \frac{23}{50}e^{10} - \frac{161}{50}e^{9} + \frac{369}{50}e^{8} + \frac{538}{25}e^{7} - \frac{407}{10}e^{6} - \frac{334}{5}e^{5} + \frac{2223}{25}e^{4} + \frac{2399}{25}e^{3} - \frac{3091}{50}e^{2} - \frac{1324}{25}e - \frac{1}{5}$
5 $[5, 5, w + 1]$ $\phantom{-}\frac{1}{5}e^{11} - \frac{2}{5}e^{10} - \frac{19}{5}e^{9} + \frac{36}{5}e^{8} + \frac{129}{5}e^{7} - 46e^{6} - 73e^{5} + \frac{609}{5}e^{4} + \frac{372}{5}e^{3} - \frac{579}{5}e^{2} - \frac{112}{5}e + 32$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{11}{25}e^{11} - \frac{17}{25}e^{10} - \frac{194}{25}e^{9} + \frac{276}{25}e^{8} + \frac{1229}{25}e^{7} - \frac{313}{5}e^{6} - \frac{672}{5}e^{5} + \frac{3584}{25}e^{4} + \frac{3742}{25}e^{3} - \frac{2714}{25}e^{2} - \frac{1492}{25}e + \frac{72}{5}$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $-1$
19 $[19, 19, -w^{3} + 3w - 1]$ $-\frac{14}{25}e^{11} + \frac{33}{25}e^{10} + \frac{256}{25}e^{9} - \frac{524}{25}e^{8} - \frac{1746}{25}e^{7} + \frac{562}{5}e^{6} + \frac{1093}{5}e^{5} - \frac{5666}{25}e^{4} - \frac{7708}{25}e^{3} + \frac{2811}{25}e^{2} + \frac{4183}{25}e + \frac{172}{5}$
23 $[23, 23, -w + 3]$ $-\frac{1}{5}e^{11} + \frac{2}{5}e^{10} + \frac{14}{5}e^{9} - \frac{36}{5}e^{8} - \frac{49}{5}e^{7} + 48e^{6} - 13e^{5} - \frac{709}{5}e^{4} + \frac{513}{5}e^{3} + \frac{869}{5}e^{2} - \frac{458}{5}e - 86$
31 $[31, 31, -w^{2} - 2w + 1]$ $\phantom{-}\frac{21}{25}e^{11} - \frac{12}{25}e^{10} - \frac{409}{25}e^{9} + \frac{136}{25}e^{8} + \frac{3019}{25}e^{7} - \frac{53}{5}e^{6} - \frac{2102}{5}e^{5} - \frac{1476}{25}e^{4} + \frac{17037}{25}e^{3} + \frac{5521}{25}e^{2} - \frac{9862}{25}e - \frac{938}{5}$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}\frac{1}{2}e^{11} - \frac{21}{2}e^{9} - e^{8} + 83e^{7} + \frac{31}{2}e^{6} - \frac{607}{2}e^{5} - \frac{173}{2}e^{4} + \frac{1001}{2}e^{3} + 202e^{2} - 291e - 154$
43 $[43, 43, 2w - 1]$ $\phantom{-}\frac{23}{25}e^{11} - \frac{6}{25}e^{10} - \frac{467}{25}e^{9} + \frac{68}{25}e^{8} + \frac{3522}{25}e^{7} - \frac{14}{5}e^{6} - \frac{2416}{5}e^{5} - \frac{1563}{25}e^{4} + \frac{18356}{25}e^{3} + \frac{5773}{25}e^{2} - \frac{9956}{25}e - \frac{974}{5}$
53 $[53, 53, -w - 3]$ $-\frac{3}{10}e^{11} + \frac{3}{5}e^{10} + \frac{47}{10}e^{9} - \frac{49}{5}e^{8} - \frac{121}{5}e^{7} + \frac{113}{2}e^{6} + \frac{85}{2}e^{5} - \frac{1347}{10}e^{4} - \frac{51}{10}e^{3} + \frac{571}{5}e^{2} - \frac{47}{5}e - 28$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $-\frac{1}{2}e^{11} + \frac{23}{2}e^{9} - 97e^{7} - \frac{11}{2}e^{6} + \frac{731}{2}e^{5} + \frac{135}{2}e^{4} - \frac{1195}{2}e^{3} - 234e^{2} + 351e + 194$
61 $[61, 61, w^{3} - 3w - 5]$ $\phantom{-}\frac{1}{50}e^{11} - \frac{11}{25}e^{10} + \frac{71}{50}e^{9} + \frac{183}{25}e^{8} - \frac{618}{25}e^{7} - \frac{463}{10}e^{6} + \frac{1303}{10}e^{5} + \frac{7119}{50}e^{4} - \frac{12803}{50}e^{3} - \frac{5362}{25}e^{2} + \frac{4089}{25}e + \frac{606}{5}$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $\phantom{-}\frac{33}{25}e^{11} - \frac{1}{25}e^{10} - \frac{682}{25}e^{9} - \frac{22}{25}e^{8} + \frac{5237}{25}e^{7} + \frac{111}{5}e^{6} - \frac{3661}{5}e^{5} - \frac{3873}{25}e^{4} + \frac{28426}{25}e^{3} + \frac{10533}{25}e^{2} - \frac{15851}{25}e - \frac{1654}{5}$
81 $[81, 3, -3]$ $-\frac{18}{25}e^{11} + \frac{21}{25}e^{10} + \frac{397}{25}e^{9} - \frac{413}{25}e^{8} - \frac{3177}{25}e^{7} + \frac{554}{5}e^{6} + \frac{2221}{5}e^{5} - \frac{6992}{25}e^{4} - \frac{16171}{25}e^{3} + \frac{4082}{25}e^{2} + \frac{8446}{25}e + \frac{284}{5}$
83 $[83, 83, -w^{3} + 5w - 3]$ $-\frac{22}{25}e^{11} + \frac{9}{25}e^{10} + \frac{438}{25}e^{9} - \frac{52}{25}e^{8} - \frac{3333}{25}e^{7} - \frac{104}{5}e^{6} + \frac{2409}{5}e^{5} + \frac{4432}{25}e^{4} - \frac{20259}{25}e^{3} - \frac{9697}{25}e^{2} + \frac{11959}{25}e + \frac{1356}{5}$
89 $[89, 89, w^{2} + 1]$ $-\frac{12}{25}e^{11} + \frac{14}{25}e^{10} + \frac{223}{25}e^{9} - \frac{267}{25}e^{8} - \frac{1468}{25}e^{7} + \frac{366}{5}e^{6} + \frac{804}{5}e^{5} - \frac{5153}{25}e^{4} - \frac{4089}{25}e^{3} + \frac{4838}{25}e^{2} + \frac{1414}{25}e - \frac{224}{5}$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $-\frac{9}{25}e^{11} - \frac{2}{25}e^{10} + \frac{211}{25}e^{9} + \frac{56}{25}e^{8} - \frac{1826}{25}e^{7} - \frac{123}{5}e^{6} + \frac{1423}{5}e^{5} + \frac{3129}{25}e^{4} - \frac{12123}{25}e^{3} - \frac{6884}{25}e^{2} + \frac{7298}{25}e + \frac{972}{5}$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $-\frac{1}{25}e^{11} + \frac{22}{25}e^{10} + \frac{29}{25}e^{9} - \frac{366}{25}e^{8} - \frac{339}{25}e^{7} + \frac{413}{5}e^{6} + \frac{357}{5}e^{5} - \frac{4519}{25}e^{4} - \frac{3972}{25}e^{3} + \frac{3074}{25}e^{2} + \frac{2872}{25}e + \frac{18}{5}$
97 $[97, 97, w^{3} - 3w - 3]$ $-\frac{12}{25}e^{11} + \frac{14}{25}e^{10} + \frac{198}{25}e^{9} - \frac{242}{25}e^{8} - \frac{1093}{25}e^{7} + \frac{306}{5}e^{6} + \frac{434}{5}e^{5} - \frac{4203}{25}e^{4} - \frac{639}{25}e^{3} + \frac{4563}{25}e^{2} - \frac{886}{25}e - \frac{364}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $1$