Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - x^{11} - 41x^{10} + 37x^{9} + 601x^{8} - 440x^{7} - 4061x^{6} + 1788x^{5} + 13740x^{4} - 1460x^{3} - 21000x^{2} - 3360x + 8208\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $-\frac{24364}{31197}e^{11} + \frac{21631}{124788}e^{10} + \frac{3629441}{124788}e^{9} - \frac{726895}{124788}e^{8} - \frac{44872501}{124788}e^{7} + \frac{6232775}{124788}e^{6} + \frac{56085119}{31197}e^{5} + \frac{3576683}{41596}e^{4} - \frac{37558511}{10399}e^{3} - \frac{23561650}{31197}e^{2} + \frac{18388130}{10399}e - \frac{1489588}{10399}$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{4141}{124788}e^{11} + \frac{61499}{62394}e^{10} + \frac{130709}{124788}e^{9} - \frac{4568209}{124788}e^{8} - \frac{1144471}{124788}e^{7} + \frac{14037047}{31197}e^{6} + \frac{971912}{31197}e^{5} - \frac{92268097}{41596}e^{4} - \frac{15411595}{41596}e^{3} + \frac{271883863}{62394}e^{2} + \frac{13448873}{10399}e - \frac{20867077}{10399}$ |
| 25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}\frac{17231}{62394}e^{11} - \frac{57811}{31197}e^{10} - \frac{1241489}{124788}e^{9} + \frac{8566099}{124788}e^{8} + \frac{14518783}{124788}e^{7} - \frac{104527277}{124788}e^{6} - \frac{69672209}{124788}e^{5} + \frac{42001080}{10399}e^{4} + \frac{70953959}{41596}e^{3} - \frac{486047551}{62394}e^{2} - \frac{30230652}{10399}e + \frac{39069782}{10399}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $-1$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{156209}{124788}e^{11} + \frac{145115}{124788}e^{10} + \frac{5811061}{124788}e^{9} - \frac{5297309}{124788}e^{8} - \frac{71747333}{124788}e^{7} + \frac{15372478}{31197}e^{6} + \frac{359944831}{124788}e^{5} - \frac{40575007}{20798}e^{4} - \frac{127838159}{20798}e^{3} + \frac{93765979}{31197}e^{2} + \frac{43117335}{10399}e - \frac{23235640}{10399}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $-\frac{1323}{41596}e^{11} + \frac{165227}{41596}e^{10} + \frac{15603}{41596}e^{9} - \frac{6134975}{41596}e^{8} + \frac{484793}{41596}e^{7} + \frac{18855366}{10399}e^{6} - \frac{5225129}{41596}e^{5} - \frac{93225068}{10399}e^{4} - \frac{10174985}{10399}e^{3} + \frac{183761773}{10399}e^{2} + \frac{51503319}{10399}e - \frac{84057404}{10399}$ |
| 59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $\phantom{-}\frac{59221}{124788}e^{11} + \frac{166321}{62394}e^{10} - \frac{1109911}{62394}e^{9} - \frac{3123890}{31197}e^{8} + \frac{13805477}{62394}e^{7} + \frac{157447717}{124788}e^{6} - \frac{132749783}{124788}e^{5} - \frac{274185977}{41596}e^{4} + \frac{20592793}{20798}e^{3} + \frac{425902816}{31197}e^{2} + \frac{32750587}{10399}e - \frac{64171584}{10399}$ |
| 59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-\frac{508003}{249576}e^{11} - \frac{347897}{249576}e^{10} + \frac{18951005}{249576}e^{9} + \frac{13412291}{249576}e^{8} - \frac{234807121}{249576}e^{7} - \frac{90574757}{124788}e^{6} + \frac{1169355305}{249576}e^{5} + \frac{94253623}{20798}e^{4} - \frac{361059775}{41596}e^{3} - \frac{330917801}{31197}e^{2} + \frac{19731577}{10399}e + \frac{38350496}{10399}$ |
| 61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $-\frac{7685}{20798}e^{11} + \frac{190239}{41596}e^{10} + \frac{264281}{20798}e^{9} - \frac{1760754}{10399}e^{8} - \frac{2822173}{20798}e^{7} + \frac{42992571}{20798}e^{6} + \frac{24032495}{41596}e^{5} - \frac{417456449}{41596}e^{4} - \frac{103633057}{41596}e^{3} + \frac{202334719}{10399}e^{2} + \frac{64343599}{10399}e - \frac{94146755}{10399}$ |
| 61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $-\frac{102497}{124788}e^{11} - \frac{108293}{62394}e^{10} + \frac{1924007}{62394}e^{9} + \frac{2037085}{31197}e^{8} - \frac{24076261}{62394}e^{7} - \frac{103623005}{124788}e^{6} + \frac{241118395}{124788}e^{5} + \frac{187205909}{41596}e^{4} - \frac{66289591}{20798}e^{3} - \frac{298861364}{31197}e^{2} - \frac{8035054}{10399}e + \frac{40897764}{10399}$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}\frac{20713}{249576}e^{11} + \frac{488435}{249576}e^{10} - \frac{761921}{249576}e^{9} - \frac{18347015}{249576}e^{8} + \frac{8978893}{249576}e^{7} + \frac{57616891}{62394}e^{6} - \frac{31135781}{249576}e^{5} - \frac{98802049}{20798}e^{4} - \frac{6766390}{10399}e^{3} + \frac{303825848}{31197}e^{2} + \frac{31786544}{10399}e - \frac{48389447}{10399}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $-\frac{119033}{62394}e^{11} + \frac{3791}{62394}e^{10} + \frac{8887781}{124788}e^{9} - \frac{120673}{124788}e^{8} - \frac{110336785}{124788}e^{7} - \frac{4571557}{124788}e^{6} + \frac{554558549}{124788}e^{5} + \frac{9979720}{10399}e^{4} - \frac{368493817}{41596}e^{3} - \frac{101858728}{31197}e^{2} + \frac{41664700}{10399}e + \frac{2726331}{10399}$ |
| 71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $\phantom{-}\frac{33717}{41596}e^{11} + \frac{189881}{41596}e^{10} - \frac{1287999}{41596}e^{9} - \frac{7091461}{41596}e^{8} + \frac{16555323}{41596}e^{7} + \frac{44227331}{20798}e^{6} - \frac{84487625}{41596}e^{5} - \frac{227430157}{20798}e^{4} + \frac{25756006}{10399}e^{3} + \frac{232053182}{10399}e^{2} + \frac{45467034}{10399}e - \frac{101708758}{10399}$ |
| 79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $\phantom{-}\frac{19694}{10399}e^{11} - \frac{52367}{41596}e^{10} - \frac{2934413}{41596}e^{9} + \frac{1900083}{41596}e^{8} + \frac{36306669}{41596}e^{7} - \frac{21553719}{41596}e^{6} - \frac{45596525}{10399}e^{5} + \frac{76140835}{41596}e^{4} + \frac{95382995}{10399}e^{3} - \frac{24253350}{10399}e^{2} - \frac{58575102}{10399}e + \frac{24425536}{10399}$ |
| 81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $-\frac{38035}{31197}e^{11} + \frac{49780}{31197}e^{10} + \frac{2797519}{62394}e^{9} - \frac{3604145}{62394}e^{8} - \frac{33827003}{62394}e^{7} + \frac{41477245}{62394}e^{6} + \frac{163874749}{62394}e^{5} - \frac{27784879}{10399}e^{4} - \frac{113966057}{20798}e^{3} + \frac{129440393}{31197}e^{2} + \frac{39502821}{10399}e - \frac{25829338}{10399}$ |
| 89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $-\frac{8359}{20798}e^{11} - \frac{23565}{20798}e^{10} + \frac{643663}{41596}e^{9} + \frac{1743639}{41596}e^{8} - \frac{8402701}{41596}e^{7} - \frac{21481605}{41596}e^{6} + \frac{44928085}{41596}e^{5} + \frac{54998743}{20798}e^{4} - \frac{80686981}{41596}e^{3} - \frac{111487327}{20798}e^{2} - \frac{1772029}{10399}e + \frac{21529210}{10399}$ |
| 89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $-\frac{33283}{124788}e^{11} + \frac{66457}{124788}e^{10} + \frac{1273637}{124788}e^{9} - \frac{2525941}{124788}e^{8} - \frac{16541149}{124788}e^{7} + \frac{15998197}{62394}e^{6} + \frac{91043771}{124788}e^{5} - \frac{26635677}{20798}e^{4} - \frac{19327385}{10399}e^{3} + \frac{80879621}{31197}e^{2} + \frac{19587261}{10399}e - \frac{16341534}{10399}$ |
| 89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $\phantom{-}\frac{127301}{124788}e^{11} + \frac{88801}{124788}e^{10} - \frac{2406011}{62394}e^{9} - \frac{1657403}{62394}e^{8} + \frac{30511951}{62394}e^{7} + \frac{42486227}{124788}e^{6} - \frac{79086874}{31197}e^{5} - \frac{41582443}{20798}e^{4} + \frac{209402237}{41596}e^{3} + \frac{139227752}{31197}e^{2} - \frac{18825233}{10399}e - \frac{12306713}{10399}$ |
| 89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $-\frac{679937}{249576}e^{11} - \frac{583981}{249576}e^{10} + \frac{25399465}{249576}e^{9} + \frac{22335043}{249576}e^{8} - \frac{315413861}{249576}e^{7} - \frac{37019404}{31197}e^{6} + \frac{1574651179}{249576}e^{5} + \frac{296399621}{41596}e^{4} - \frac{481056789}{41596}e^{3} - \frac{508355446}{31197}e^{2} + \frac{20789544}{10399}e + \frac{61386392}{10399}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $1$ |