[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion .
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(4027\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{174} - 21 T_{2}^{173} - 47 T_{2}^{172} + 4028 T_{2}^{171} - 14815 T_{2}^{170} - 356264 T_{2}^{169} + \cdots + 164087296 \)
T2^174 - 21*T2^173 - 47*T2^172 + 4028*T2^171 - 14815*T2^170 - 356264*T2^169 + 2497249*T2^168 + 18519900*T2^167 - 204827396*T2^166 - 559068857*T2^165 + 11254093380*T2^164 + 3976373272*T2^163 - 460402823635*T2^162 + 571083808070*T2^161 + 14761386214074*T2^160 - 37666965848360*T2^159 - 380995308700667*T2^158 + 1465863157654468*T2^157 + 7996483735274988*T2^156 - 43050352063882449*T2^155 - 135253557845492382*T2^154 + 1029172943363336574*T2^153 + 1756604800690828658*T2^152 - 20760851531365853250*T2^151 - 14283872727118922351*T2^150 + 360787447950779945253*T2^149 - 40062885522325910378*T2^148 - 5472583651533251318023*T2^147 + 4340122673637145535883*T2^146 + 73065337692979644524488*T2^145 - 104006191276266680616832*T2^144 - 862818902249801695214628*T2^143 + 1773131368383266027873864*T2^142 + 9025849465235968934831627*T2^141 - 24769295015047150340215384*T2^140 - 83434292863651713766321543*T2^139 + 297943271248169516655950902*T2^138 + 675620013602298780545681467*T2^137 - 3161220083617507898172978683*T2^136 - 4692351345271799978078060361*T2^135 + 29997473069183892969735860558*T2^134 + 26497881983149930755847775932*T2^133 - 256823367383493820420844474891*T2^132 - 101205896068777447150530138479*T2^131 + 1995511453176203415318165058222*T2^130 - 49714774647463905509340827050*T2^129 - 14127688866923589546820841072388*T2^128 + 5663182741089206909080357973361*T2^127 + 91370280712852865877973127897933*T2^126 - 68893676986802336145428697989857*T2^125 - 540581952715365522108986590271039*T2^124 + 595595368355710283822784825138599*T2^123 + 2926455018539089058645469351699374*T2^122 - 4278153292743985740813824566689592*T2^121 - 14479940784122008180800625217927415*T2^120 + 26873878953064048306205156450198108*T2^119 + 65295234828084242577467247401409544*T2^118 - 151138949167476387661699402080416194*T2^117 - 266831274258914104259813312501762910*T2^116 + 770843835419411979702171612765809318*T2^115 + 977853035349902815506487064316001794*T2^114 - 3593167436396769153807054146682560028*T2^113 - 3148377308964615242440735316147774775*T2^112 + 15384729754182591174346331105155495093*T2^111 + 8506299959970453950712312131697407521*T2^110 - 60709585872923167596666323709041973405*T2^109 - 16795763073811045145336050554114111274*T2^108 + 221283578056279870798686535756929726382*T2^107 + 7263189000792641717458829125530003934*T2^106 - 746075648090095018483561647482770664483*T2^105 + 141101458775215017701224195116695393451*T2^104 + 2328598209216237513609769678132628016407*T2^103 - 925413013955485406433338102689425257490*T2^102 - 6729349059688277107863988449221357878244*T2^101 + 4031766675625679325557431817356276076270*T2^100 + 17999683198537075135241547598549974560881*T2^99 - 14420297370200170259233838512934869728745*T2^98 - 44519687036716356668690352660250362157854*T2^97 + 45006956232396640574153389944312867030783*T2^96 + 101647448921584358642558884187499858259590*T2^95 - 125820325485595842005455155168014011872761*T2^94 - 213663966667671301296277594211109118731101*T2^93 + 319328902837171325306216733870604538466662*T2^92 + 411776338839369417335849411323984086229042*T2^91 - 741478134051748611521170030577473422591439*T2^90 - 722903366262867217781257672352874774461411*T2^89 + 1582616737048541104138210096613492031734974*T2^88 + 1143871412339815361376567800755717388548605*T2^87 - 3114207985857224674232947851962972952530961*T2^86 - 1600602236372132725356313806412987008791140*T2^85 + 5659817879180836703325226686773880214394205*T2^84 + 1903837457451546080833018089533982512780800*T2^83 - 9510299557647831276403280125648579560507625*T2^82 - 1728867576317945852223798347175217614364327*T2^81 + 14781954604397158414785562862004675923849099*T2^80 + 655912967014453969468612934446131343560500*T2^79 - 21253651229786974959617171637104972056770559*T2^78 + 1704718743553831468972779843161166781997593*T2^77 + 28259141012272825154750160547164386174026723*T2^76 - 5520273447020726492284290067938906797544306*T2^75 - 34723874168194849322788163927991948745668182*T2^74 + 10550465406813326550294758151511972799282107*T2^73 + 39394057555188399144777446412683853766859038*T2^72 - 16078988568986897590675233087343063728230286*T2^71 - 41212297161920447867294296401450565297485619*T2^70 + 21044398330438538030900164446829250489882966*T2^69 + 39695532755130380439327104296060143217336644*T2^68 - 24359291182376599901862282984446132022898391*T2^67 - 35135944388319833496797858290129834674909512*T2^66 + 25292857857752020906055627739877869592475371*T2^65 + 28514213712080076102818867398743731998147767*T2^64 - 23735307043416634858252681967025329220263636*T2^63 - 21157619828091012067676026829298147789762424*T2^62 + 20212663484602303069432974655610942289439776*T2^61 + 14305309452009228517733630106671646968728767*T2^60 - 15652765583078773834787869243772306541420000*T2^59 - 8776539741636994180691893790117901646399980*T2^58 + 11032133421423149749171187689129566913429715*T2^57 + 4859627451404820676256020760800971950122371*T2^56 - 7076486157668987950185056549121754507020070*T2^55 - 2411071127446554505296814614218370812518888*T2^54 + 4128385515749254886970645398746780750241133*T2^53 + 1060999774652515030631706979513366160869507*T2^52 - 2187998746372113223066868159671139004192548*T2^51 - 407646445031986719719319356686212124970281*T2^50 + 1051814078140267940030910124589692794844258*T2^49 + 133029045771944321519979659999836408124577*T2^48 - 457740188415016795441990258979660641503634*T2^47 - 34759732277842657566181438337422498853141*T2^46 + 179929967175579697370723891323187846679974*T2^45 + 6040203149983089760516839787520456974731*T2^44 - 63718369294428825876770182179135099160079*T2^43 + 91443732589597856056670559813545863977*T2^42 + 20268719896693824783142196756502066267579*T2^41 - 600895615315548083185492747431139212300*T2^40 - 5772331365210047857148172125906379006374*T2^39 + 297032911429969026375642727085050222611*T2^38 + 1466286210002571089526164005044046846853*T2^37 - 98446306291237640192915464556723026357*T2^36 - 330818315444592571665028990164566882193*T2^35 + 25435461091365823804028536314724688512*T2^34 + 65971090881717589030828709741753776398*T2^33 - 5334786261508056305053822173817183014*T2^32 - 11562595283461136686213540930579033472*T2^31 + 916541666741659343617530065704245242*T2^30 + 1769240899710203231657739787209900403*T2^29 - 128016030174574785657344133217773088*T2^28 - 234445364427096980434683827494944466*T2^27 + 14185952799174989470621926659645077*T2^26 + 26638387571883530248801148343554716*T2^25 - 1178477306412635733225927438301837*T2^24 - 2563195919678637583629380294579557*T2^23 + 62029122031934097761074831200206*T2^22 + 205564910481927845395168297369642*T2^21 - 231486223870987000068544041006*T2^20 - 13456882977614516971888381013549*T2^19 - 326448415298031320706045608521*T2^18 + 699013815775574181306477434506*T2^17 + 35951451460498125206054659631*T2^16 - 27674992211008089515874907376*T2^15 - 2225988425498441994640241375*T2^14 + 784820818003799146781497727*T2^13 + 88543330415839217721745761*T2^12 - 14269792732400872022346280*T2^11 - 2217729148778243021603870*T2^10 + 126690742675262329227056*T2^9 + 31471780602164969458516*T2^8 + 85618059790567356400*T2^7 - 199261554058612864392*T2^6 - 6386349128718113552*T2^5 + 409033196288260608*T2^4 + 20389252841434048*T2^3 + 164172661922816*T2^2 + 387270655488*T2 + 164087296
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4027))\).