Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + x^{14} - 44x^{13} - 48x^{12} + 749x^{11} + 834x^{10} - 6296x^{9} - 6701x^{8} + 27904x^{7} + 26318x^{6} - 65288x^{5} - 50272x^{4} + 74848x^{3} + 41888x^{2} - 32512x - 9984\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-\frac{6732783913}{9056363046424}e^{14} - \frac{31545190941}{18112726092848}e^{13} + \frac{272607280503}{9056363046424}e^{12} + \frac{1376210933925}{18112726092848}e^{11} - \frac{4040986138561}{9056363046424}e^{10} - \frac{21692223228799}{18112726092848}e^{9} + \frac{53342808091399}{18112726092848}e^{8} + \frac{38354797287929}{4528181523212}e^{7} - \frac{148664206882373}{18112726092848}e^{6} - \frac{493741567539345}{18112726092848}e^{5} + \frac{53619918376403}{9056363046424}e^{4} + \frac{344293606652761}{9056363046424}e^{3} + \frac{20332211751357}{2264090761606}e^{2} - \frac{42036338635345}{2264090761606}e - \frac{9260023913616}{1132045380803}$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $-\frac{43679712783}{144901808742784}e^{14} - \frac{147722215201}{144901808742784}e^{13} + \frac{422666059067}{72450904371392}e^{12} + \frac{1839251371781}{36225452185696}e^{11} + \frac{8112578452309}{144901808742784}e^{10} - \frac{15967842369951}{18112726092848}e^{9} - \frac{36643459703823}{18112726092848}e^{8} + \frac{979645063749587}{144901808742784}e^{7} + \frac{1156829896989189}{72450904371392}e^{6} - \frac{1679580751377307}{72450904371392}e^{5} - \frac{1686698069738455}{36225452185696}e^{4} + \frac{571512732777703}{18112726092848}e^{3} + \frac{428796286408051}{9056363046424}e^{2} - \frac{23908729090215}{2264090761606}e - \frac{10724398857867}{1132045380803}$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $\phantom{-}\frac{353747603921}{72450904371392}e^{14} - \frac{37269864329}{36225452185696}e^{13} - \frac{14725421837835}{72450904371392}e^{12} + \frac{145475906599}{18112726092848}e^{11} + \frac{234213899597201}{72450904371392}e^{10} + \frac{15156784045707}{72450904371392}e^{9} - \frac{896056859057773}{36225452185696}e^{8} - \frac{170123222253049}{72450904371392}e^{7} + \frac{6867367710713599}{72450904371392}e^{6} + \frac{149275127217733}{36225452185696}e^{5} - \frac{6294131354533891}{36225452185696}e^{4} + \frac{14433225648684}{1132045380803}e^{3} + \frac{1141372437688481}{9056363046424}e^{2} - \frac{30761143740518}{1132045380803}e - \frac{18328492931009}{1132045380803}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $-\frac{286923058303}{144901808742784}e^{14} + \frac{318009592231}{144901808742784}e^{13} + \frac{5872653793135}{72450904371392}e^{12} - \frac{2669191832267}{36225452185696}e^{11} - \frac{185422017741163}{144901808742784}e^{10} + \frac{1114496078591}{1132045380803}e^{9} + \frac{178172387711285}{18112726092848}e^{8} - \frac{986476570671277}{144901808742784}e^{7} - \frac{2789949463009303}{72450904371392}e^{6} + \frac{1859185352420797}{72450904371392}e^{5} + \frac{2672938770856737}{36225452185696}e^{4} - \frac{850722694657285}{18112726092848}e^{3} - \frac{534429971539779}{9056363046424}e^{2} + \frac{68973555024697}{2264090761606}e + \frac{13391649695361}{1132045380803}$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $-1$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $-\frac{373374884555}{144901808742784}e^{14} + \frac{244522885807}{144901808742784}e^{13} + \frac{7916012723513}{72450904371392}e^{12} - \frac{2144509809891}{36225452185696}e^{11} - \frac{258513416057127}{144901808742784}e^{10} + \frac{31931366080123}{36225452185696}e^{9} + \frac{64351651020221}{4528181523212}e^{8} - \frac{1055497729623729}{144901808742784}e^{7} - \frac{4204456161016217}{72450904371392}e^{6} + \frac{2447183257159889}{72450904371392}e^{5} + \frac{4219949866600791}{36225452185696}e^{4} - \frac{1336583438841077}{18112726092848}e^{3} - \frac{813461748646363}{9056363046424}e^{2} + \frac{117956887287577}{2264090761606}e + \frac{5524432114117}{1132045380803}$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $\phantom{-}\frac{475242033707}{289803617485568}e^{14} + \frac{559299737161}{289803617485568}e^{13} - \frac{9523437120757}{144901808742784}e^{12} - \frac{6693948980513}{72450904371392}e^{11} + \frac{280106278538535}{289803617485568}e^{10} + \frac{114651518681075}{72450904371392}e^{9} - \frac{28809746545419}{4528181523212}e^{8} - \frac{3563694571019119}{289803617485568}e^{7} + \frac{2610161167249533}{144901808742784}e^{6} + \frac{6517968061221303}{144901808742784}e^{5} - \frac{1125576593420267}{72450904371392}e^{4} - \frac{2691066408089367}{36225452185696}e^{3} - \frac{179886984735241}{18112726092848}e^{2} + \frac{198045859109437}{4528181523212}e + \frac{35792267358321}{2264090761606}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $\phantom{-}\frac{357833608619}{289803617485568}e^{14} - \frac{2182092395663}{289803617485568}e^{13} - \frac{7797420498545}{144901808742784}e^{12} + \frac{21217966336903}{72450904371392}e^{11} + \frac{284738714499527}{289803617485568}e^{10} - \frac{313273538443947}{72450904371392}e^{9} - \frac{170970571039105}{18112726092848}e^{8} + \frac{8786327483446961}{289803617485568}e^{7} + \frac{7054024072554329}{144901808742784}e^{6} - \frac{15130087695614457}{144901808742784}e^{5} - \frac{8969426885973895}{72450904371392}e^{4} + \frac{6097659481504745}{36225452185696}e^{3} + \frac{2335409498024843}{18112726092848}e^{2} - \frac{433659517099071}{4528181523212}e - \frac{70903162989579}{2264090761606}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}\frac{453942195093}{144901808742784}e^{14} - \frac{439481118103}{144901808742784}e^{13} - \frac{4728217663205}{36225452185696}e^{12} + \frac{3582043159113}{36225452185696}e^{11} + \frac{304378489450721}{144901808742784}e^{10} - \frac{90583296135457}{72450904371392}e^{9} - \frac{597071771617243}{36225452185696}e^{8} + \frac{1149156662141095}{144901808742784}e^{7} + \frac{2382947759946595}{36225452185696}e^{6} - \frac{1960028448626095}{72450904371392}e^{5} - \frac{575985590173827}{4528181523212}e^{4} + \frac{846671160059561}{18112726092848}e^{3} + \frac{442010759205903}{4528181523212}e^{2} - \frac{76145616026925}{2264090761606}e - \frac{13720176859610}{1132045380803}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{276410246563}{36225452185696}e^{14} + \frac{646794824189}{72450904371392}e^{13} - \frac{22855191499509}{72450904371392}e^{12} - \frac{7355650324901}{18112726092848}e^{11} + \frac{176807354458297}{36225452185696}e^{10} + \frac{471923800889687}{72450904371392}e^{9} - \frac{1277077284328643}{36225452185696}e^{8} - \frac{1657680633804469}{36225452185696}e^{7} + \frac{8839832308397213}{72450904371392}e^{6} + \frac{1272380027152295}{9056363046424}e^{5} - \frac{6899552900395025}{36225452185696}e^{4} - \frac{769987424005613}{4528181523212}e^{3} + \frac{884330615505713}{9056363046424}e^{2} + \frac{58610035868915}{1132045380803}e + \frac{15090644231380}{1132045380803}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{15214379707}{4528181523212}e^{14} - \frac{115646605903}{72450904371392}e^{13} - \frac{10306344839547}{72450904371392}e^{12} + \frac{876754990167}{18112726092848}e^{11} + \frac{41981614951629}{18112726092848}e^{10} - \frac{45743505522291}{72450904371392}e^{9} - \frac{665406490310397}{36225452185696}e^{8} + \frac{90272207874221}{18112726092848}e^{7} + \frac{5368039737770715}{72450904371392}e^{6} - \frac{433235727619689}{18112726092848}e^{5} - \frac{5295635650105283}{36225452185696}e^{4} + \frac{242832585748805}{4528181523212}e^{3} + \frac{1093499806391509}{9056363046424}e^{2} - \frac{43913774078211}{1132045380803}e - \frac{25878911907785}{1132045380803}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $-\frac{161036722917}{289803617485568}e^{14} - \frac{1706959209483}{289803617485568}e^{13} + \frac{3085535556225}{144901808742784}e^{12} + \frac{17526976536275}{72450904371392}e^{11} - \frac{68529651449913}{289803617485568}e^{10} - \frac{134455075093553}{36225452185696}e^{9} + \frac{5584772606293}{36225452185696}e^{8} + \frac{7677096348496529}{289803617485568}e^{7} + \frac{1615512425641991}{144901808742784}e^{6} - \frac{13062508655510193}{144901808742784}e^{5} - \frac{4088577582246869}{72450904371392}e^{4} + \frac{5023574786383305}{36225452185696}e^{3} + \frac{1486387786432197}{18112726092848}e^{2} - \frac{336672059025201}{4528181523212}e - \frac{44556020381697}{2264090761606}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{781045319965}{144901808742784}e^{14} + \frac{915729547291}{144901808742784}e^{13} - \frac{16232099816557}{72450904371392}e^{12} - \frac{10435333797591}{36225452185696}e^{11} + \frac{506637103070385}{144901808742784}e^{10} + \frac{41930388550747}{9056363046424}e^{9} - \frac{463679516501009}{18112726092848}e^{8} - \frac{4721572613281193}{144901808742784}e^{7} + \frac{6558917939355901}{72450904371392}e^{6} + \frac{7218843673900833}{72450904371392}e^{5} - \frac{5314305041832975}{36225452185696}e^{4} - \frac{2080555152233685}{18112726092848}e^{3} + \frac{787213226943847}{9056363046424}e^{2} + \frac{55614447439483}{2264090761606}e - \frac{5770146957695}{1132045380803}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $\phantom{-}\frac{1729819324647}{289803617485568}e^{14} - \frac{2063173610303}{289803617485568}e^{13} - \frac{37136466303279}{144901808742784}e^{12} + \frac{18866461464191}{72450904371392}e^{11} + \frac{1247158824782307}{289803617485568}e^{10} - \frac{69245799556155}{18112726092848}e^{9} - \frac{1298385593019921}{36225452185696}e^{8} + \frac{8345899037593685}{289803617485568}e^{7} + \frac{22517025444221991}{144901808742784}e^{6} - \frac{16688362445036629}{144901808742784}e^{5} - \frac{24390864247695421}{72450904371392}e^{4} + \frac{7968660854232645}{36225452185696}e^{3} + \frac{5612820705373421}{18112726092848}e^{2} - \frac{673071937292613}{4528181523212}e - \frac{145020989788889}{2264090761606}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $\phantom{-}\frac{134075146717}{36225452185696}e^{14} - \frac{80675712533}{36225452185696}e^{13} - \frac{170913824541}{1132045380803}e^{12} + \frac{1137840323423}{18112726092848}e^{11} + \frac{85106016624913}{36225452185696}e^{10} - \frac{3157612644983}{4528181523212}e^{9} - \frac{318013618434291}{18112726092848}e^{8} + \frac{159141511456987}{36225452185696}e^{7} + \frac{1195034147501633}{18112726092848}e^{6} - \frac{41065252580553}{2264090761606}e^{5} - \frac{1108479559545003}{9056363046424}e^{4} + \frac{352519500792167}{9056363046424}e^{3} + \frac{112410167760512}{1132045380803}e^{2} - \frac{66769455523973}{2264090761606}e - \frac{19864018379536}{1132045380803}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $-\frac{33187911967}{72450904371392}e^{14} - \frac{172232523983}{18112726092848}e^{13} + \frac{631703478151}{72450904371392}e^{12} + \frac{3621545923123}{9056363046424}e^{11} + \frac{11903925157737}{72450904371392}e^{10} - \frac{455729769323015}{72450904371392}e^{9} - \frac{185369384720937}{36225452185696}e^{8} + \frac{3351410835603671}{72450904371392}e^{7} + \frac{3099807157206337}{72450904371392}e^{6} - \frac{5936021683646953}{36225452185696}e^{5} - \frac{5059695579226533}{36225452185696}e^{4} + \frac{2414421906434647}{9056363046424}e^{3} + \frac{1543375144156547}{9056363046424}e^{2} - \frac{180270077815562}{1132045380803}e - \frac{51014220007503}{1132045380803}$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $\phantom{-}\frac{846041879841}{144901808742784}e^{14} + \frac{666349460527}{144901808742784}e^{13} - \frac{17502890463641}{72450904371392}e^{12} - \frac{7812780961213}{36225452185696}e^{11} + \frac{543199308146629}{144901808742784}e^{10} + \frac{62657457626277}{18112726092848}e^{9} - \frac{123260329307153}{4528181523212}e^{8} - \frac{3411717296422701}{144901808742784}e^{7} + \frac{6873056027923941}{72450904371392}e^{6} + \frac{4823521162494665}{72450904371392}e^{5} - \frac{5390147033833383}{36225452185696}e^{4} - \frac{1249575887719659}{18112726092848}e^{3} + \frac{715500244790103}{9056363046424}e^{2} + \frac{21203863845312}{1132045380803}e + \frac{3638600049347}{1132045380803}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{172369337713}{36225452185696}e^{14} + \frac{109339708471}{36225452185696}e^{13} - \frac{3381119385123}{18112726092848}e^{12} - \frac{398130423965}{2264090761606}e^{11} + \frac{97649977945141}{36225452185696}e^{10} + \frac{3792748592477}{1132045380803}e^{9} - \frac{158056888041411}{9056363046424}e^{8} - \frac{1010789001827973}{36225452185696}e^{7} + \frac{883638028699225}{18112726092848}e^{6} + \frac{1950401955342919}{18112726092848}e^{5} - \frac{399705574451967}{9056363046424}e^{4} - \frac{210551464086796}{1132045380803}e^{3} - \frac{30420605579333}{2264090761606}e^{2} + \frac{124415224242570}{1132045380803}e + \frac{23376652155886}{1132045380803}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{1525568235547}{144901808742784}e^{14} - \frac{676127376217}{144901808742784}e^{13} + \frac{32212769890909}{72450904371392}e^{12} + \frac{8853359429893}{36225452185696}e^{11} - \frac{1038026184671543}{144901808742784}e^{10} - \frac{148085501225811}{36225452185696}e^{9} + \frac{503104045082103}{9056363046424}e^{8} + \frac{3987167452215007}{144901808742784}e^{7} - \frac{15714614248324749}{72450904371392}e^{6} - \frac{4998887299469375}{72450904371392}e^{5} + \frac{14909682403851043}{36225452185696}e^{4} + \frac{636161338067259}{18112726092848}e^{3} - \frac{2850922404288923}{9056363046424}e^{2} + \frac{83612582232567}{2264090761606}e + \frac{47656687431233}{1132045380803}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $1$ |