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 | $[97, 97, w^{3} - 3w - 3]$ | $-\frac{12}{25}e^{11} + \frac{14}{25}e^{10} + \frac{198}{25}e^{9} - \frac{242}{25}e^{8} - \frac{1093}{25}e^{7} + \frac{306}{5}e^{6} + \frac{434}{5}e^{5} - \frac{4203}{25}e^{4} - \frac{639}{25}e^{3} + \frac{4563}{25}e^{2} - \frac{886}{25}e - \frac{364}{5}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{3} + w^{2} + 3w - 1]$ | $1$ |