Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 4x^{10} - 11x^{9} + 51x^{8} + 31x^{7} - 195x^{6} - 4x^{5} + 212x^{4} - 12x^{3} - 85x^{2} + 4x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{21}{25}e^{10} - \frac{76}{25}e^{9} - \frac{254}{25}e^{8} + \frac{954}{25}e^{7} + \frac{943}{25}e^{6} - \frac{3481}{25}e^{5} - \frac{1172}{25}e^{4} + \frac{3071}{25}e^{3} + \frac{781}{25}e^{2} - \frac{647}{25}e - \frac{172}{25}$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $-\frac{4}{5}e^{10} + \frac{19}{5}e^{9} + \frac{31}{5}e^{8} - \frac{231}{5}e^{7} + \frac{33}{5}e^{6} + \frac{799}{5}e^{5} - \frac{512}{5}e^{4} - \frac{604}{5}e^{3} + \frac{381}{5}e^{2} + \frac{128}{5}e - \frac{57}{5}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $\phantom{-}\frac{14}{25}e^{10} - \frac{84}{25}e^{9} - \frac{36}{25}e^{8} + \frac{986}{25}e^{7} - \frac{1013}{25}e^{6} - \frac{3179}{25}e^{5} + \frac{5052}{25}e^{4} + \frac{1739}{25}e^{3} - \frac{4371}{25}e^{2} - \frac{173}{25}e + \frac{977}{25}$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{16}{25}e^{10} - \frac{71}{25}e^{9} - \frac{134}{25}e^{8} + \frac{834}{25}e^{7} + \frac{3}{25}e^{6} - \frac{2626}{25}e^{5} + \frac{1513}{25}e^{4} + \frac{1091}{25}e^{3} - \frac{999}{25}e^{2} - \frac{62}{25}e + \frac{138}{25}$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{26}{25}e^{10} + \frac{56}{25}e^{9} + \frac{474}{25}e^{8} - \frac{799}{25}e^{7} - \frac{3133}{25}e^{6} + \frac{3536}{25}e^{5} + \frac{8382}{25}e^{4} - \frac{4776}{25}e^{3} - \frac{6411}{25}e^{2} + \frac{1357}{25}e + \frac{1282}{25}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{2}{25}e^{10} - \frac{37}{25}e^{9} + \frac{102}{25}e^{8} + \frac{373}{25}e^{7} - \frac{1434}{25}e^{6} - \frac{722}{25}e^{5} + \frac{4986}{25}e^{4} - \frac{1223}{25}e^{3} - \frac{3003}{25}e^{2} + \frac{761}{25}e + \frac{411}{25}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{17}{25}e^{10} - \frac{102}{25}e^{9} - \frac{33}{25}e^{8} + \frac{1158}{25}e^{7} - \frac{1339}{25}e^{6} - \frac{3387}{25}e^{5} + \frac{6281}{25}e^{4} + \frac{592}{25}e^{3} - \frac{4513}{25}e^{2} + \frac{481}{25}e + \frac{831}{25}$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{13}{25}e^{10} - \frac{22}{25}e^{9} + \frac{437}{25}e^{8} + \frac{138}{25}e^{7} - \frac{4054}{25}e^{6} + \frac{343}{25}e^{5} + \frac{13141}{25}e^{4} - \frac{2463}{25}e^{3} - \frac{10843}{25}e^{2} + \frac{1041}{25}e + \frac{2316}{25}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $-\frac{4}{5}e^{10} + \frac{19}{5}e^{9} + \frac{31}{5}e^{8} - \frac{231}{5}e^{7} + \frac{28}{5}e^{6} + \frac{809}{5}e^{5} - \frac{462}{5}e^{4} - \frac{674}{5}e^{3} + \frac{251}{5}e^{2} + \frac{198}{5}e - \frac{2}{5}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{36}{25}e^{10} + \frac{216}{25}e^{9} + \frac{89}{25}e^{8} - \frac{2514}{25}e^{7} + \frac{2612}{25}e^{6} + \frac{7921}{25}e^{5} - \frac{12673}{25}e^{4} - \frac{3711}{25}e^{3} + \frac{9779}{25}e^{2} + \frac{227}{25}e - \frac{1923}{25}$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}\frac{133}{25}e^{10} - \frac{548}{25}e^{9} - \frac{1342}{25}e^{8} + \frac{6717}{25}e^{7} + \frac{2739}{25}e^{6} - \frac{23438}{25}e^{5} + \frac{3669}{25}e^{4} + \frac{17758}{25}e^{3} - \frac{3162}{25}e^{2} - \frac{3331}{25}e + \frac{569}{25}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{39}{25}e^{10} - \frac{184}{25}e^{9} - \frac{286}{25}e^{8} + \frac{2161}{25}e^{7} - \frac{488}{25}e^{6} - \frac{6854}{25}e^{5} + \frac{5427}{25}e^{4} + \frac{3039}{25}e^{3} - \frac{3796}{25}e^{2} + \frac{152}{25}e + \frac{552}{25}$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $\phantom{-}\frac{11}{5}e^{10} - \frac{46}{5}e^{9} - \frac{109}{5}e^{8} + \frac{564}{5}e^{7} + \frac{208}{5}e^{6} - \frac{1981}{5}e^{5} + \frac{328}{5}e^{4} + \frac{1581}{5}e^{3} - \frac{154}{5}e^{2} - \frac{387}{5}e - \frac{7}{5}$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-\frac{38}{25}e^{10} + \frac{103}{25}e^{9} + \frac{612}{25}e^{8} - \frac{1412}{25}e^{7} - \frac{3554}{25}e^{6} + \frac{5968}{25}e^{5} + \frac{8416}{25}e^{4} - \frac{7613}{25}e^{3} - \frac{5668}{25}e^{2} + \frac{2316}{25}e + \frac{1016}{25}$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}\frac{162}{25}e^{10} - \frac{622}{25}e^{9} - \frac{1813}{25}e^{8} + \frac{7688}{25}e^{7} + \frac{5571}{25}e^{6} - \frac{27257}{25}e^{5} - \frac{3709}{25}e^{4} + \frac{21887}{25}e^{3} + \frac{3782}{25}e^{2} - \frac{4409}{25}e - \frac{1434}{25}$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{29}{25}e^{10} - \frac{199}{25}e^{9} + \frac{29}{25}e^{8} + \frac{2271}{25}e^{7} - \frac{3293}{25}e^{6} - \frac{6844}{25}e^{5} + \frac{14047}{25}e^{4} + \frac{2179}{25}e^{3} - \frac{9831}{25}e^{2} + \frac{497}{25}e + \frac{1597}{25}$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $-\frac{67}{25}e^{10} + \frac{402}{25}e^{9} + \frac{158}{25}e^{8} - \frac{4658}{25}e^{7} + \frac{4964}{25}e^{6} + \frac{14487}{25}e^{5} - \frac{23981}{25}e^{4} - \frac{6067}{25}e^{3} + \frac{18438}{25}e^{2} + \frac{19}{25}e - \frac{3506}{25}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}\frac{44}{25}e^{10} - \frac{89}{25}e^{9} - \frac{831}{25}e^{8} + \frac{1331}{25}e^{7} + \frac{5602}{25}e^{6} - \frac{6334}{25}e^{5} - \frac{14808}{25}e^{4} + \frac{9869}{25}e^{3} + \frac{10009}{25}e^{2} - \frac{3183}{25}e - \frac{1758}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $-1$ |