Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w^{2} - w - 3]$ |
| Dimension: | $11$ |
| 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:
| \(x^{11} - 2x^{10} - 33x^{9} + 64x^{8} + 374x^{7} - 662x^{6} - 1768x^{5} + 2510x^{4} + 3519x^{3} - 2646x^{2} - 2932x - 200\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-\frac{29158751}{9726238420}e^{10} + \frac{19652909}{2431559605}e^{9} + \frac{817060649}{9726238420}e^{8} - \frac{126906273}{486311921}e^{7} - \frac{1660953576}{2431559605}e^{6} + \frac{6585009772}{2431559605}e^{5} + \frac{6293270923}{4863119210}e^{4} - \frac{49953091447}{4863119210}e^{3} + \frac{12915425617}{9726238420}e^{2} + \frac{28088519492}{2431559605}e + \frac{1041787423}{486311921}$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $-\frac{6104306}{486311921}e^{10} + \frac{29160617}{972623842}e^{9} + \frac{375618711}{972623842}e^{8} - \frac{454134549}{486311921}e^{7} - \frac{1858525710}{486311921}e^{6} + \frac{9012551375}{972623842}e^{5} + \frac{6573924206}{486311921}e^{4} - \frac{15820762146}{486311921}e^{3} - \frac{6508586523}{486311921}e^{2} + \frac{13624649402}{486311921}e + \frac{3307044654}{486311921}$ |
| 13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-\frac{9143953}{1945247684}e^{10} - \frac{2209169}{972623842}e^{9} + \frac{302664613}{1945247684}e^{8} + \frac{38112704}{486311921}e^{7} - \frac{1676074107}{972623842}e^{6} - \frac{496133939}{486311921}e^{5} + \frac{6860976933}{972623842}e^{4} + \frac{5467738241}{972623842}e^{3} - \frac{12570473035}{1945247684}e^{2} - \frac{5496535094}{486311921}e - \frac{1996011231}{486311921}$ |
| 16 | $[16, 2, 2]$ | $-\frac{886497}{1945247684}e^{10} - \frac{2623837}{972623842}e^{9} + \frac{31380507}{1945247684}e^{8} + \frac{28618549}{486311921}e^{7} - \frac{99305443}{486311921}e^{6} - \frac{196144161}{972623842}e^{5} + \frac{1099954973}{972623842}e^{4} - \frac{907457343}{486311921}e^{3} - \frac{6559826795}{1945247684}e^{2} + \frac{6995430947}{972623842}e + \frac{2697866543}{486311921}$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{55746989}{9726238420}e^{10} + \frac{68525987}{4863119210}e^{9} + \frac{1724544981}{9726238420}e^{8} - \frac{424336917}{972623842}e^{7} - \frac{4257541729}{2431559605}e^{6} + \frac{10412489378}{2431559605}e^{5} + \frac{28689112087}{4863119210}e^{4} - \frac{36022327709}{2431559605}e^{3} - \frac{38019517407}{9726238420}e^{2} + \frac{33279806793}{2431559605}e + \frac{2048878741}{486311921}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-\frac{66461967}{9726238420}e^{10} + \frac{42069561}{4863119210}e^{9} + \frac{2216085973}{9726238420}e^{8} - \frac{273120671}{972623842}e^{7} - \frac{6333482192}{2431559605}e^{6} + \frac{14315818683}{4863119210}e^{5} + \frac{28989297868}{2431559605}e^{4} - \frac{56617563549}{4863119210}e^{3} - \frac{179991860211}{9726238420}e^{2} + \frac{35112972564}{2431559605}e + \frac{3399903767}{486311921}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{47650727}{9726238420}e^{10} - \frac{21283539}{4863119210}e^{9} + \frac{1462794843}{9726238420}e^{8} + \frac{63928248}{486311921}e^{7} - \frac{3753742907}{2431559605}e^{6} - \frac{7441890657}{4863119210}e^{5} + \frac{29493421721}{4863119210}e^{4} + \frac{39593831151}{4863119210}e^{3} - \frac{74991832831}{9726238420}e^{2} - \frac{39373390221}{2431559605}e + \frac{394994687}{486311921}$ |
| 19 | $[19, 19, w^{2} - w - 2]$ | $\phantom{-}\frac{16182637}{4863119210}e^{10} + \frac{38362244}{2431559605}e^{9} - \frac{299658189}{2431559605}e^{8} - \frac{488707003}{972623842}e^{7} + \frac{8280380153}{4863119210}e^{6} + \frac{26442321379}{4863119210}e^{5} - \frac{50450377907}{4863119210}e^{4} - \frac{54600033886}{2431559605}e^{3} + \frac{58375122833}{2431559605}e^{2} + \frac{63353329972}{2431559605}e - \frac{2061421541}{486311921}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $-\frac{3949917}{4863119210}e^{10} - \frac{34670234}{2431559605}e^{9} + \frac{169318523}{4863119210}e^{8} + \frac{220632153}{486311921}e^{7} - \frac{1315244239}{2431559605}e^{6} - \frac{12012354782}{2431559605}e^{5} + \frac{7419566456}{2431559605}e^{4} + \frac{51832616611}{2431559605}e^{3} - \frac{12024162191}{4863119210}e^{2} - \frac{69025543137}{2431559605}e - \frac{4719199118}{486311921}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-1$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{10590994}{2431559605}e^{10} + \frac{77303667}{4863119210}e^{9} - \frac{350823086}{2431559605}e^{8} - \frac{485478507}{972623842}e^{7} + \frac{4129710461}{2431559605}e^{6} + \frac{26087259231}{4863119210}e^{5} - \frac{40683573203}{4863119210}e^{4} - \frac{54611350204}{2431559605}e^{3} + \frac{36449921122}{2431559605}e^{2} + \frac{70520106258}{2431559605}e - \frac{293071334}{486311921}$ |
| 43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $-\frac{105554669}{9726238420}e^{10} + \frac{86546146}{2431559605}e^{9} + \frac{3192047081}{9726238420}e^{8} - \frac{553628988}{486311921}e^{7} - \frac{15483385753}{4863119210}e^{6} + \frac{28390481888}{2431559605}e^{5} + \frac{26591335496}{2431559605}e^{4} - \frac{102855863044}{2431559605}e^{3} - \frac{91724329157}{9726238420}e^{2} + \frac{88275417583}{2431559605}e + \frac{3111352341}{486311921}$ |
| 47 | $[47, 47, w^{3} - 7w - 4]$ | $\phantom{-}\frac{81161009}{9726238420}e^{10} - \frac{7461366}{2431559605}e^{9} - \frac{2665022171}{9726238420}e^{8} + \frac{41803995}{486311921}e^{7} + \frac{14861104183}{4863119210}e^{6} - \frac{1340120443}{2431559605}e^{5} - \frac{32193932186}{2431559605}e^{4} - \frac{1887265057}{4863119210}e^{3} + \frac{159110148387}{9726238420}e^{2} + \frac{34962254359}{4863119210}e + \frac{3273689167}{486311921}$ |
| 53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $\phantom{-}\frac{401119}{1945247684}e^{10} - \frac{8090637}{486311921}e^{9} + \frac{37259783}{1945247684}e^{8} + \frac{262127618}{486311921}e^{7} - \frac{658329283}{972623842}e^{6} - \frac{5577715823}{972623842}e^{5} + \frac{6015872141}{972623842}e^{4} + \frac{21652688853}{972623842}e^{3} - \frac{32453677779}{1945247684}e^{2} - \frac{11556096996}{486311921}e + \frac{3883315673}{486311921}$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{42160539}{9726238420}e^{10} + \frac{25031613}{4863119210}e^{9} - \frac{1615822461}{9726238420}e^{8} - \frac{100954422}{486311921}e^{7} + \frac{5441980819}{2431559605}e^{6} + \frac{6940431592}{2431559605}e^{5} - \frac{30460821026}{2431559605}e^{4} - \frac{37519903046}{2431559605}e^{3} + \frac{245634599337}{9726238420}e^{2} + \frac{64126730997}{2431559605}e - \frac{2683207648}{486311921}$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{40843001}{2431559605}e^{10} + \frac{230228557}{4863119210}e^{9} + \frac{1194013069}{2431559605}e^{8} - \frac{739376933}{486311921}e^{7} - \frac{10595674674}{2431559605}e^{6} + \frac{38277229123}{2431559605}e^{5} + \frac{53114813337}{4863119210}e^{4} - \frac{286856122043}{4863119210}e^{3} + \frac{27299741079}{4863119210}e^{2} + \frac{137368769123}{2431559605}e - \frac{2078967475}{486311921}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $-\frac{6950559}{2431559605}e^{10} + \frac{77559034}{2431559605}e^{9} + \frac{153306116}{2431559605}e^{8} - \frac{959590045}{972623842}e^{7} - \frac{529206217}{4863119210}e^{6} + \frac{24117321002}{2431559605}e^{5} - \frac{9786951071}{2431559605}e^{4} - \frac{175530011937}{4863119210}e^{3} + \frac{45739316928}{2431559605}e^{2} + \frac{79091701177}{2431559605}e - \frac{4022554755}{486311921}$ |
| 81 | $[81, 3, -3]$ | $-\frac{66047701}{9726238420}e^{10} + \frac{71871999}{2431559605}e^{9} + \frac{1973797279}{9726238420}e^{8} - \frac{884871821}{972623842}e^{7} - \frac{9633700677}{4863119210}e^{6} + \frac{21747713207}{2431559605}e^{5} + \frac{37814146873}{4863119210}e^{4} - \frac{77481437946}{2431559605}e^{3} - \frac{131295112873}{9726238420}e^{2} + \frac{82362652607}{2431559605}e + \frac{4467858649}{486311921}$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $\phantom{-}\frac{38158603}{1945247684}e^{10} - \frac{17517954}{486311921}e^{9} - \frac{1173357183}{1945247684}e^{8} + \frac{1072807097}{972623842}e^{7} + \frac{5805389503}{972623842}e^{6} - \frac{10165195907}{972623842}e^{5} - \frac{10016374344}{486311921}e^{4} + \frac{32197799965}{972623842}e^{3} + \frac{27699936117}{1945247684}e^{2} - \frac{10411116325}{486311921}e + \frac{2811725965}{486311921}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^{2} - w - 3]$ | $1$ |