Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[139, 139, -w^{5} - w^{4} + 8w^{3} + 12w^{2} - 3w - 5]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 4x^{7} - 86x^{6} + 230x^{5} + 1887x^{4} - 3026x^{3} - 13513x^{2} + 5886x + 23413\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $\phantom{-}e$ |
| 29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $-\frac{10420688}{36415534529}e^{7} + \frac{54924961}{36415534529}e^{6} + \frac{745145019}{36415534529}e^{5} - \frac{3441133101}{36415534529}e^{4} - \frac{7670573816}{36415534529}e^{3} + \frac{60147393495}{36415534529}e^{2} - \frac{59252990171}{36415534529}e - \frac{309187269012}{36415534529}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $-\frac{116674243}{72831069058}e^{7} + \frac{397327482}{36415534529}e^{6} + \frac{8735560717}{72831069058}e^{5} - \frac{26409955399}{36415534529}e^{4} - \frac{145482436735}{72831069058}e^{3} + \frac{771151968267}{72831069058}e^{2} + \frac{502356588707}{72831069058}e - \frac{1648571187205}{72831069058}$ |
| 29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $\phantom{-}\frac{1173411}{72831069058}e^{7} - \frac{39150819}{36415534529}e^{6} + \frac{182017883}{72831069058}e^{5} + \frac{2906501637}{36415534529}e^{4} - \frac{12162881955}{72831069058}e^{3} - \frac{83635806791}{72831069058}e^{2} + \frac{103472393507}{72831069058}e + \frac{425949671075}{72831069058}$ |
| 29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $-\frac{197736327}{145662138116}e^{7} + \frac{275114391}{36415534529}e^{6} + \frac{14157578575}{145662138116}e^{5} - \frac{32853860947}{72831069058}e^{4} - \frac{180929123019}{145662138116}e^{3} + \frac{878448301443}{145662138116}e^{2} - \frac{7987021459}{145662138116}e - \frac{2228401389747}{145662138116}$ |
| 29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $\phantom{-}\frac{24858292}{36415534529}e^{7} - \frac{577876507}{145662138116}e^{6} - \frac{1859842344}{36415534529}e^{5} + \frac{18633993083}{72831069058}e^{4} + \frac{109504954609}{145662138116}e^{3} - \frac{292173827359}{72831069058}e^{2} + \frac{6928538635}{145662138116}e + \frac{2212215179403}{145662138116}$ |
| 41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $\phantom{-}\frac{1340189}{72831069058}e^{7} - \frac{12874567}{36415534529}e^{6} + \frac{33295425}{36415534529}e^{5} + \frac{341839435}{36415534529}e^{4} - \frac{2959790593}{36415534529}e^{3} + \frac{25497428116}{36415534529}e^{2} + \frac{13115236197}{36415534529}e - \frac{454974466191}{72831069058}$ |
| 41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $-\frac{124291177}{72831069058}e^{7} + \frac{873640349}{72831069058}e^{6} + \frac{8595282343}{72831069058}e^{5} - \frac{57007763399}{72831069058}e^{4} - \frac{54252602000}{36415534529}e^{3} + \frac{412446500759}{36415534529}e^{2} + \frac{102227077341}{72831069058}e - \frac{2051383296939}{72831069058}$ |
| 41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $-\frac{257281897}{72831069058}e^{7} + \frac{679026460}{36415534529}e^{6} + \frac{39463867847}{145662138116}e^{5} - \frac{165850731377}{145662138116}e^{4} - \frac{647029388595}{145662138116}e^{3} + \frac{573481918432}{36415534529}e^{2} + \frac{969694812213}{72831069058}e - \frac{5212089632975}{145662138116}$ |
| 41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $\phantom{-}\frac{38329297}{72831069058}e^{7} + \frac{33878787}{36415534529}e^{6} - \frac{1821030379}{36415534529}e^{5} - \frac{4401900911}{36415534529}e^{4} + \frac{36707120949}{36415534529}e^{3} + \frac{72474254708}{36415534529}e^{2} - \frac{148154639533}{36415534529}e - \frac{193713383863}{72831069058}$ |
| 41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $-\frac{40842897}{72831069058}e^{7} + \frac{18146599}{36415534529}e^{6} + \frac{3393452025}{72831069058}e^{5} + \frac{1153559839}{36415534529}e^{4} - \frac{55331778757}{72831069058}e^{3} - \frac{112307558857}{72831069058}e^{2} + \frac{166606413165}{72831069058}e + \frac{805386731443}{72831069058}$ |
| 41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $\phantom{-}\frac{9580833}{72831069058}e^{7} + \frac{128481685}{72831069058}e^{6} - \frac{579008484}{36415534529}e^{5} - \frac{12630518981}{72831069058}e^{4} + \frac{32320057309}{72831069058}e^{3} + \frac{256334204813}{72831069058}e^{2} - \frac{172182691839}{36415534529}e - \frac{858975709783}{72831069058}$ |
| 49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $\phantom{-}\frac{100940135}{72831069058}e^{7} - \frac{551073137}{72831069058}e^{6} - \frac{7488205559}{72831069058}e^{5} + \frac{16411170316}{36415534529}e^{4} + \frac{54914337096}{36415534529}e^{3} - \frac{398722135463}{72831069058}e^{2} - \frac{94872524100}{36415534529}e + \frac{292496149857}{36415534529}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{807373201}{145662138116}e^{7} - \frac{3976128351}{145662138116}e^{6} - \frac{15504935349}{36415534529}e^{5} + \frac{235315777533}{145662138116}e^{4} + \frac{998601595581}{145662138116}e^{3} - \frac{3152919076679}{145662138116}e^{2} - \frac{1537748016525}{72831069058}e + \frac{7352356348221}{145662138116}$ |
| 71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $-\frac{2337387}{1776367538}e^{7} + \frac{8351281}{888183769}e^{6} + \frac{176713919}{1776367538}e^{5} - \frac{560215178}{888183769}e^{4} - \frac{3174177783}{1776367538}e^{3} + \frac{15874565397}{1776367538}e^{2} + \frac{15142989489}{1776367538}e - \frac{28679482617}{1776367538}$ |
| 71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $\phantom{-}\frac{48669917}{72831069058}e^{7} - \frac{164500418}{36415534529}e^{6} - \frac{3647053431}{72831069058}e^{5} + \frac{20745999531}{72831069058}e^{4} + \frac{65232504343}{72831069058}e^{3} - \frac{134515682770}{36415534529}e^{2} - \frac{167968504442}{36415534529}e + \frac{433391994837}{36415534529}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-\frac{15388553}{6621006278}e^{7} + \frac{92753525}{6621006278}e^{6} + \frac{576043745}{3310503139}e^{5} - \frac{2974730796}{3310503139}e^{4} - \frac{18543913949}{6621006278}e^{3} + \frac{44438527714}{3310503139}e^{2} + \frac{61030849603}{6621006278}e - \frac{114601927757}{3310503139}$ |
| 71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $-\frac{66957659}{72831069058}e^{7} + \frac{1011433421}{145662138116}e^{6} + \frac{5015876029}{72831069058}e^{5} - \frac{34185917715}{72831069058}e^{4} - \frac{181459918861}{145662138116}e^{3} + \frac{239489070454}{36415534529}e^{2} + \frac{720317439817}{145662138116}e - \frac{1376251471239}{145662138116}$ |
| 71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $\phantom{-}\frac{445059143}{145662138116}e^{7} - \frac{727092369}{36415534529}e^{6} - \frac{32961646719}{145662138116}e^{5} + \frac{46327619436}{36415534529}e^{4} + \frac{540994414647}{145662138116}e^{3} - \frac{2477635821097}{145662138116}e^{2} - \frac{2142624095091}{145662138116}e + \frac{4785613591409}{145662138116}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $\phantom{-}\frac{41724140}{36415534529}e^{7} - \frac{837347151}{72831069058}e^{6} - \frac{2600915159}{36415534529}e^{5} + \frac{59314883077}{72831069058}e^{4} + \frac{53173425243}{72831069058}e^{3} - \frac{937200560375}{72831069058}e^{2} + \frac{32189667912}{36415534529}e + \frac{1355553945133}{36415534529}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $139$ | $[139, 139, -w^{5} - w^{4} + 8w^{3} + 12w^{2} - 3w - 5]$ | $1$ |