Properties

Label 4.4.19429.1-16.1-c
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $14$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $41$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{14} + 3x^{13} - 25x^{12} - 77x^{11} + 223x^{10} + 721x^{9} - 849x^{8} - 3038x^{7} + 1203x^{6} + 5664x^{5} - 26x^{4} - 3826x^{3} - 658x^{2} + 585x + 67\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}\frac{963666832}{558766699055}e^{13} - \frac{1045510568}{558766699055}e^{12} - \frac{25081022059}{558766699055}e^{11} + \frac{30020386544}{558766699055}e^{10} + \frac{222495853113}{558766699055}e^{9} - \frac{307470012094}{558766699055}e^{8} - \frac{136136033842}{111753339811}e^{7} + \frac{1326623660444}{558766699055}e^{6} - \frac{435507791997}{558766699055}e^{5} - \frac{2160718233953}{558766699055}e^{4} + \frac{4816366868139}{558766699055}e^{3} + \frac{156045109899}{111753339811}e^{2} - \frac{4337214891871}{558766699055}e - \frac{243033427573}{558766699055}$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-\frac{10442801989}{6705200388660}e^{13} - \frac{10800861807}{558766699055}e^{12} + \frac{144685666313}{6705200388660}e^{11} + \frac{1684620462241}{3352600194330}e^{10} + \frac{85831746373}{2235066796220}e^{9} - \frac{5331666590627}{1117533398110}e^{8} - \frac{683394689235}{447013359244}e^{7} + \frac{136083640260017}{6705200388660}e^{6} + \frac{6718203405919}{1117533398110}e^{5} - \frac{125077099894117}{3352600194330}e^{4} - \frac{9550892183272}{1676300097165}e^{3} + \frac{4879156619399}{223506679622}e^{2} + \frac{31164712448}{1676300097165}e - \frac{3719224232703}{2235066796220}$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{23628654551}{1676300097165}e^{13} - \frac{9718004507}{558766699055}e^{12} + \frac{662978558047}{1676300097165}e^{11} + \frac{697580670013}{1676300097165}e^{10} - \frac{2345588597808}{558766699055}e^{9} - \frac{1936768822991}{558766699055}e^{8} + \frac{2357778398216}{111753339811}e^{7} + \frac{19612357287808}{1676300097165}e^{6} - \frac{28366289070378}{558766699055}e^{5} - \frac{19985048156716}{1676300097165}e^{4} + \frac{85418503391083}{1676300097165}e^{3} - \frac{820609890774}{111753339811}e^{2} - \frac{23168822084192}{1676300097165}e + \frac{2788945077133}{558766699055}$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}\frac{5586260555}{223506679622}e^{13} + \frac{10781758771}{223506679622}e^{12} - \frac{74530065382}{111753339811}e^{11} - \frac{134084053594}{111753339811}e^{10} + \frac{1481489741637}{223506679622}e^{9} + \frac{2388421496341}{223506679622}e^{8} - \frac{3437997154581}{111753339811}e^{7} - \frac{9229891073629}{223506679622}e^{6} + \frac{15271071887081}{223506679622}e^{5} + \frac{14358559373667}{223506679622}e^{4} - \frac{14936187510643}{223506679622}e^{3} - \frac{5328138356251}{223506679622}e^{2} + \frac{5098675376627}{223506679622}e - \frac{292834816652}{111753339811}$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, -w + 2]$ $-\frac{47816831386}{1676300097165}e^{13} - \frac{48201751019}{1117533398110}e^{12} + \frac{2562410669359}{3352600194330}e^{11} + \frac{1800982065698}{1676300097165}e^{10} - \frac{4241049220883}{558766699055}e^{9} - \frac{10883195636997}{1117533398110}e^{8} + \frac{7758255728211}{223506679622}e^{7} + \frac{67292728024868}{1676300097165}e^{6} - \frac{81972181755711}{1117533398110}e^{5} - \frac{256685275560397}{3352600194330}e^{4} + \frac{209177042050951}{3352600194330}e^{3} + \frac{13301555730661}{223506679622}e^{2} - \frac{53104864582409}{3352600194330}e - \frac{9930566477509}{1117533398110}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{57956203117}{1676300097165}e^{13} - \frac{75200195813}{1117533398110}e^{12} + \frac{3047242683523}{3352600194330}e^{11} + \frac{2815911420791}{1676300097165}e^{10} - \frac{4922504104981}{558766699055}e^{9} - \frac{16903645587599}{1117533398110}e^{8} + \frac{8743761277861}{223506679622}e^{7} + \frac{101056476889541}{1676300097165}e^{6} - \frac{89487805660837}{1117533398110}e^{5} - \frac{346118671799089}{3352600194330}e^{4} + \frac{221593007982877}{3352600194330}e^{3} + \frac{13544620440315}{223506679622}e^{2} - \frac{41137735221563}{3352600194330}e - \frac{10577713738773}{1117533398110}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}\frac{1673584043}{447013359244}e^{13} + \frac{4100252027}{335260019433}e^{12} - \frac{44309177291}{447013359244}e^{11} - \frac{211185868643}{670520038866}e^{10} + \frac{1331576529245}{1341040077732}e^{9} + \frac{654949891453}{223506679622}e^{8} - \frac{2173074253469}{447013359244}e^{7} - \frac{5335457677727}{447013359244}e^{6} + \frac{8538437849701}{670520038866}e^{5} + \frac{4479105125299}{223506679622}e^{4} - \frac{5955083071475}{335260019433}e^{3} - \frac{7436560948763}{670520038866}e^{2} + \frac{827937188753}{111753339811}e + \frac{6648583766501}{1341040077732}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{34490378612}{1676300097165}e^{13} + \frac{108234554312}{1676300097165}e^{12} - \frac{881176951669}{1676300097165}e^{11} - \frac{2778555333821}{1676300097165}e^{10} + \frac{8278803314843}{1676300097165}e^{9} + \frac{8679178490912}{558766699055}e^{8} - \frac{2388307364343}{111753339811}e^{7} - \frac{110034027671326}{1676300097165}e^{6} + \frac{72829071395078}{1676300097165}e^{5} + \frac{207159166879147}{1676300097165}e^{4} - \frac{20271749311162}{558766699055}e^{3} - \frac{28610954944397}{335260019433}e^{2} + \frac{5684358279614}{1676300097165}e + \frac{17836741900097}{1676300097165}$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}\frac{357795404789}{6705200388660}e^{13} + \frac{384725606857}{3352600194330}e^{12} - \frac{9320833799083}{6705200388660}e^{11} - \frac{9566006979601}{3352600194330}e^{10} + \frac{89401574647241}{6705200388660}e^{9} + \frac{14252880519721}{558766699055}e^{8} - \frac{26237623178127}{447013359244}e^{7} - \frac{671592648098137}{6705200388660}e^{6} + \frac{201993175747574}{1676300097165}e^{5} + \frac{276486083595181}{1676300097165}e^{4} - \frac{116792368539467}{1117533398110}e^{3} - \frac{27355812451247}{335260019433}e^{2} + \frac{86671364985889}{3352600194330}e + \frac{16057356945899}{6705200388660}$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}\frac{132646113249}{2235066796220}e^{13} + \frac{165874218328}{1676300097165}e^{12} - \frac{3589358351973}{2235066796220}e^{11} - \frac{8087216512483}{3352600194330}e^{10} + \frac{108978480936163}{6705200388660}e^{9} + \frac{23364536108071}{1117533398110}e^{8} - \frac{34455608600635}{447013359244}e^{7} - \frac{174977258159557}{2235066796220}e^{6} + \frac{586165271118389}{3352600194330}e^{5} + \frac{134836834040137}{1117533398110}e^{4} - \frac{288413840330119}{1676300097165}e^{3} - \frac{38577684370763}{670520038866}e^{2} + \frac{31479520533897}{558766699055}e + \frac{35540011626487}{6705200388660}$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{473271799883}{6705200388660}e^{13} - \frac{83329226609}{558766699055}e^{12} + \frac{12681700928371}{6705200388660}e^{11} + \frac{12599697543557}{3352600194330}e^{10} - \frac{42299037758509}{2235066796220}e^{9} - \frac{38254993556779}{1117533398110}e^{8} + \frac{39700497059515}{447013359244}e^{7} + \frac{924741903375739}{6705200388660}e^{6} - \frac{223924764804907}{1117533398110}e^{5} - \frac{789854771884529}{3352600194330}e^{4} + \frac{328141953306541}{1676300097165}e^{3} + \frac{27953312119165}{223506679622}e^{2} - \frac{89353721456354}{1676300097165}e - \frac{21418195388361}{2235066796220}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{95954184113}{6705200388660}e^{13} - \frac{10321519529}{558766699055}e^{12} + \frac{2993508634321}{6705200388660}e^{11} + \frac{1663928021897}{3352600194330}e^{10} - \frac{12217497461019}{2235066796220}e^{9} - \frac{5404282250229}{1117533398110}e^{8} + \frac{14906828476005}{447013359244}e^{7} + \frac{136754141830309}{6705200388660}e^{6} - \frac{116894525845787}{1117533398110}e^{5} - \frac{108054456377999}{3352600194330}e^{4} + \frac{250311335840911}{1676300097165}e^{3} + \frac{710759269423}{223506679622}e^{2} - \frac{93702054870524}{1676300097165}e + \frac{9787857008369}{2235066796220}$
53 $[53, 53, -w - 3]$ $\phantom{-}\frac{10158050039}{223506679622}e^{13} + \frac{50035257275}{670520038866}e^{12} - \frac{141448153604}{111753339811}e^{11} - \frac{637478828651}{335260019433}e^{10} + \frac{8931073944503}{670520038866}e^{9} + \frac{3928432347541}{223506679622}e^{8} - \frac{7451542387373}{111753339811}e^{7} - \frac{16118205834833}{223506679622}e^{6} + \frac{109514018486507}{670520038866}e^{5} + \frac{28035175742241}{223506679622}e^{4} - \frac{118333560128273}{670520038866}e^{3} - \frac{44120906765575}{670520038866}e^{2} + \frac{11543522685897}{223506679622}e - \frac{217689072374}{335260019433}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}\frac{70589660051}{1676300097165}e^{13} + \frac{338447584267}{3352600194330}e^{12} - \frac{3801613589459}{3352600194330}e^{11} - \frac{4296634508168}{1676300097165}e^{10} + \frac{19323677372789}{1676300097165}e^{9} + \frac{26409466657537}{1117533398110}e^{8} - \frac{12560076687069}{223506679622}e^{7} - \frac{162957280042573}{1676300097165}e^{6} + \frac{458483348134993}{3352600194330}e^{5} + \frac{580309242707537}{3352600194330}e^{4} - \frac{168144801158747}{1117533398110}e^{3} - \frac{68746001729275}{670520038866}e^{2} + \frac{150464138477539}{3352600194330}e + \frac{26499408900397}{3352600194330}$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-\frac{8536332076}{1676300097165}e^{13} - \frac{106268853617}{3352600194330}e^{12} + \frac{490725257929}{3352600194330}e^{11} + \frac{1418262024478}{1676300097165}e^{10} - \frac{2863767093739}{1676300097165}e^{9} - \frac{9292956854577}{1117533398110}e^{8} + \frac{2367609689539}{223506679622}e^{7} + \frac{61812347867858}{1676300097165}e^{6} - \frac{120667208426753}{3352600194330}e^{5} - \frac{237517547442607}{3352600194330}e^{4} + \frac{63011442196677}{1117533398110}e^{3} + \frac{28826541395723}{670520038866}e^{2} - \frac{61934245352219}{3352600194330}e - \frac{2256976958417}{3352600194330}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}\frac{219458053657}{6705200388660}e^{13} + \frac{173308706728}{1676300097165}e^{12} - \frac{5575626103769}{6705200388660}e^{11} - \frac{8850733402343}{3352600194330}e^{10} + \frac{51406894246693}{6705200388660}e^{9} + \frac{27250963424341}{1117533398110}e^{8} - \frac{14155059591061}{447013359244}e^{7} - \frac{666948110388821}{6705200388660}e^{6} + \frac{196727773750049}{3352600194330}e^{5} + \frac{577471793541901}{3352600194330}e^{4} - \frac{24933637739953}{558766699055}e^{3} - \frac{66154050050723}{670520038866}e^{2} + \frac{18054577918141}{1676300097165}e + \frac{93362307405157}{6705200388660}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{68256959509}{1676300097165}e^{13} + \frac{198498675653}{3352600194330}e^{12} - \frac{3671085875251}{3352600194330}e^{11} - \frac{2511742630837}{1676300097165}e^{10} + \frac{18208023119956}{1676300097165}e^{9} + \frac{15583315851963}{1117533398110}e^{8} - \frac{10906454019399}{223506679622}e^{7} - \frac{100630442383952}{1676300097165}e^{6} + \frac{321577541815517}{3352600194330}e^{5} + \frac{409934252308783}{3352600194330}e^{4} - \frac{69027816883693}{1117533398110}e^{3} - \frac{69115558061489}{670520038866}e^{2} + \frac{6426540305621}{3352600194330}e + \frac{54618454444703}{3352600194330}$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{7571606107}{335260019433}e^{13} + \frac{67273437487}{670520038866}e^{12} - \frac{389033028187}{670520038866}e^{11} - \frac{293042897442}{111753339811}e^{10} + \frac{1866866591735}{335260019433}e^{9} + \frac{5609212461351}{223506679622}e^{8} - \frac{5708682623199}{223506679622}e^{7} - \frac{36266147723303}{335260019433}e^{6} + \frac{39489858717103}{670520038866}e^{5} + \frac{136880013130063}{670520038866}e^{4} - \frac{39900576776075}{670520038866}e^{3} - \frac{86816819961899}{670520038866}e^{2} + \frac{2518655823563}{670520038866}e + \frac{7291531443523}{670520038866}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $-1$