Base field 4.4.6809.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{2} - w + 3]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 4x^{13} - 15x^{12} + 74x^{11} + 60x^{10} - 495x^{9} + 52x^{8} + 1446x^{7} - 674x^{6} - 1805x^{5} + 892x^{4} + 1023x^{3} - 334x^{2} - 200x + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 4w]$ | $-\frac{764}{3805}e^{13} + \frac{1736}{3805}e^{12} + \frac{2860}{761}e^{11} - \frac{31371}{3805}e^{10} - \frac{19562}{761}e^{9} + \frac{40260}{761}e^{8} + \frac{301932}{3805}e^{7} - \frac{539294}{3805}e^{6} - \frac{445874}{3805}e^{5} + \frac{107110}{761}e^{4} + \frac{374652}{3805}e^{3} - \frac{166102}{3805}e^{2} - \frac{97129}{3805}e + \frac{1842}{761}$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 3]$ | $-\frac{1864}{3805}e^{13} + \frac{5371}{3805}e^{12} + \frac{6420}{761}e^{11} - \frac{96241}{3805}e^{10} - \frac{37627}{761}e^{9} + \frac{121809}{761}e^{8} + \frac{410397}{3805}e^{7} - \frac{1591099}{3805}e^{6} - \frac{202589}{3805}e^{5} + \frac{300129}{761}e^{4} + \frac{28882}{3805}e^{3} - \frac{457787}{3805}e^{2} - \frac{6244}{3805}e + \frac{4518}{761}$ |
| 11 | $[11, 11, w^{3} - 5w + 1]$ | $-\frac{466}{3805}e^{13} + \frac{2294}{3805}e^{12} + \frac{844}{761}e^{11} - \frac{38329}{3805}e^{10} + \frac{4101}{761}e^{9} + \frac{42438}{761}e^{8} - \frac{316902}{3805}e^{7} - \frac{394921}{3805}e^{6} + \frac{1000484}{3805}e^{5} - \frac{1258}{761}e^{4} - \frac{873637}{3805}e^{3} + \frac{189002}{3805}e^{2} + \frac{211519}{3805}e - \frac{8383}{761}$ |
| 17 | $[17, 17, -w^{3} - w^{2} + 5w + 4]$ | $\phantom{-}\frac{506}{761}e^{13} - \frac{1596}{761}e^{12} - \frac{8188}{761}e^{11} + \frac{28166}{761}e^{10} + \frac{41930}{761}e^{9} - \frac{173332}{761}e^{8} - \frac{56819}{761}e^{7} + \frac{425766}{761}e^{6} - \frac{69980}{761}e^{5} - \frac{333066}{761}e^{4} + \frac{69104}{761}e^{3} + \frac{61043}{761}e^{2} - \frac{7486}{761}e + \frac{5108}{761}$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-\frac{249}{761}e^{13} + \frac{1020}{761}e^{12} + \frac{3545}{761}e^{11} - \frac{17915}{761}e^{10} - \frac{12058}{761}e^{9} + \frac{108968}{761}e^{8} - \frac{25248}{761}e^{7} - \frac{259644}{761}e^{6} + \frac{167308}{761}e^{5} + \frac{182519}{761}e^{4} - \frac{142934}{761}e^{3} - \frac{25303}{761}e^{2} + \frac{32289}{761}e - \frac{1136}{761}$ |
| 29 | $[29, 29, -w^{2} - w + 3]$ | $-1$ |
| 31 | $[31, 31, -w^{3} + 6w + 2]$ | $\phantom{-}\frac{3051}{3805}e^{13} - \frac{9124}{3805}e^{12} - \frac{9971}{761}e^{11} + \frac{160714}{3805}e^{10} + \frac{52240}{761}e^{9} - \frac{197436}{761}e^{8} - \frac{392498}{3805}e^{7} + \frac{2423951}{3805}e^{6} - \frac{309134}{3805}e^{5} - \frac{385635}{761}e^{4} + \frac{354827}{3805}e^{3} + \frac{462403}{3805}e^{2} - \frac{33374}{3805}e - \frac{5820}{761}$ |
| 43 | $[43, 43, w^{3} - 6w]$ | $-\frac{221}{3805}e^{13} - \frac{1231}{3805}e^{12} + \frac{1919}{761}e^{11} + \frac{19946}{3805}e^{10} - \frac{25100}{761}e^{9} - \frac{20344}{761}e^{8} + \frac{693848}{3805}e^{7} + \frac{132174}{3805}e^{6} - \frac{1661286}{3805}e^{5} + \frac{36663}{761}e^{4} + \frac{1427813}{3805}e^{3} - \frac{125373}{3805}e^{2} - \frac{382016}{3805}e + \frac{1758}{761}$ |
| 47 | $[47, 47, 2w^{3} - 9w]$ | $-\frac{221}{3805}e^{13} - \frac{1231}{3805}e^{12} + \frac{1919}{761}e^{11} + \frac{19946}{3805}e^{10} - \frac{25100}{761}e^{9} - \frac{20344}{761}e^{8} + \frac{693848}{3805}e^{7} + \frac{132174}{3805}e^{6} - \frac{1657481}{3805}e^{5} + \frac{37424}{761}e^{4} + \frac{1389763}{3805}e^{3} - \frac{148203}{3805}e^{2} - \frac{305916}{3805}e + \frac{4802}{761}$ |
| 47 | $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ | $-\frac{2539}{3805}e^{13} + \frac{4056}{3805}e^{12} + \frac{10680}{761}e^{11} - \frac{77416}{3805}e^{10} - \frac{85396}{761}e^{9} + \frac{108428}{761}e^{8} + \frac{1609202}{3805}e^{7} - \frac{1685924}{3805}e^{6} - \frac{2853694}{3805}e^{5} + \frac{435989}{761}e^{4} + \frac{2053872}{3805}e^{3} - \frac{781452}{3805}e^{2} - \frac{388654}{3805}e + \frac{6506}{761}$ |
| 53 | $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ | $\phantom{-}\frac{1091}{3805}e^{13} + \frac{51}{3805}e^{12} - \frac{5634}{761}e^{11} + \frac{2719}{3805}e^{10} + \frac{55265}{761}e^{9} - \frac{11756}{761}e^{8} - \frac{1271828}{3805}e^{7} + \frac{379846}{3805}e^{6} + \frac{2709611}{3805}e^{5} - \frac{179894}{761}e^{4} - \frac{2212753}{3805}e^{3} + \frac{485128}{3805}e^{2} + \frac{540821}{3805}e - \frac{10087}{761}$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-\frac{3388}{3805}e^{13} + \frac{10587}{3805}e^{12} + \frac{11117}{761}e^{11} - \frac{187167}{3805}e^{10} - \frac{59293}{761}e^{9} + \frac{231598}{761}e^{8} + \frac{496774}{3805}e^{7} - \frac{2891478}{3805}e^{6} + \frac{104142}{3805}e^{5} + \frac{483910}{761}e^{4} - \frac{26511}{3805}e^{3} - \frac{607079}{3805}e^{2} - \frac{108793}{3805}e + \frac{1941}{761}$ |
| 59 | $[59, 59, 3w^{3} - 15w - 5]$ | $\phantom{-}\frac{1054}{3805}e^{13} - \frac{4666}{3805}e^{12} - \frac{2830}{761}e^{11} + \frac{80781}{3805}e^{10} + \frac{7548}{761}e^{9} - \frac{95859}{761}e^{8} + \frac{175088}{3805}e^{7} + \frac{1077784}{3805}e^{6} - \frac{831956}{3805}e^{5} - \frac{113506}{761}e^{4} + \frac{644718}{3805}e^{3} - \frac{149018}{3805}e^{2} - \frac{131506}{3805}e + \frac{13392}{761}$ |
| 71 | $[71, 71, w^{3} - 3w - 3]$ | $\phantom{-}\frac{1757}{3805}e^{13} - \frac{2558}{3805}e^{12} - \frac{7402}{761}e^{11} + \frac{47308}{3805}e^{10} + \frac{59568}{761}e^{9} - \frac{63279}{761}e^{8} - \frac{1145526}{3805}e^{7} + \frac{921382}{3805}e^{6} + \frac{2157122}{3805}e^{5} - \frac{221963}{761}e^{4} - \frac{1834546}{3805}e^{3} + \frac{469536}{3805}e^{2} + \frac{466707}{3805}e - \frac{10354}{761}$ |
| 81 | $[81, 3, -3]$ | $-\frac{2339}{3805}e^{13} + \frac{7546}{3805}e^{12} + \frac{7473}{761}e^{11} - \frac{135841}{3805}e^{10} - \frac{36659}{761}e^{9} + \frac{173160}{761}e^{8} + \frac{178172}{3805}e^{7} - \frac{2288894}{3805}e^{6} + \frac{626886}{3805}e^{5} + \frac{443649}{761}e^{4} - \frac{770218}{3805}e^{3} - \frac{756437}{3805}e^{2} + \frac{174911}{3805}e + \frac{10793}{761}$ |
| 83 | $[83, 83, -2w^{3} + 8w + 3]$ | $\phantom{-}\frac{3686}{3805}e^{13} - \frac{6224}{3805}e^{12} - \frac{15416}{761}e^{11} + \frac{119329}{3805}e^{10} + \frac{122528}{761}e^{9} - \frac{168540}{761}e^{8} - \frac{2298963}{3805}e^{7} + \frac{2666766}{3805}e^{6} + \frac{4097036}{3805}e^{5} - \frac{721648}{761}e^{4} - \frac{3086228}{3805}e^{3} + \frac{1563373}{3805}e^{2} + \frac{721841}{3805}e - \frac{25864}{761}$ |
| 89 | $[89, 89, -2w^{3} + 11w - 2]$ | $\phantom{-}\frac{2666}{3805}e^{13} - \frac{9564}{3805}e^{12} - \frac{7964}{761}e^{11} + \frac{168069}{3805}e^{10} + \frac{32790}{761}e^{9} - \frac{205536}{761}e^{8} + \frac{39092}{3805}e^{7} + \frac{2494726}{3805}e^{6} - \frac{1163629}{3805}e^{5} - \frac{377931}{761}e^{4} + \frac{944962}{3805}e^{3} + \frac{325878}{3805}e^{2} - \frac{119329}{3805}e + \frac{9880}{761}$ |
| 101 | $[101, 101, 2w^{3} - w^{2} - 10w]$ | $-\frac{625}{761}e^{13} + \frac{699}{761}e^{12} + \frac{14057}{761}e^{11} - \frac{13855}{761}e^{10} - \frac{121800}{761}e^{9} + \frac{103047}{761}e^{8} + \frac{505066}{761}e^{7} - \frac{352488}{761}e^{6} - \frac{1001696}{761}e^{5} + \frac{527543}{761}e^{4} + \frac{816327}{761}e^{3} - \frac{228945}{761}e^{2} - \frac{198332}{761}e + \frac{19294}{761}$ |
| 101 | $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ | $-\frac{2094}{3805}e^{13} + \frac{7826}{3805}e^{12} + \frac{6265}{761}e^{11} - \frac{138446}{3805}e^{10} - \frac{25527}{761}e^{9} + \frac{171258}{761}e^{8} - \frac{59118}{3805}e^{7} - \frac{2130884}{3805}e^{6} + \frac{1092826}{3805}e^{5} + \frac{350678}{761}e^{4} - \frac{1139878}{3805}e^{3} - \frac{412547}{3805}e^{2} + \frac{304326}{3805}e + \frac{1909}{761}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{2} - w + 3]$ | $1$ |