[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
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
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
\(2\)
\(1\)
\(11\)
\(1\)
\(197\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{17} - 5 T_{3}^{16} - 19 T_{3}^{15} + 121 T_{3}^{14} + 112 T_{3}^{13} - 1172 T_{3}^{12} - 25 T_{3}^{11} + 5845 T_{3}^{10} - 2233 T_{3}^{9} - 16035 T_{3}^{8} + 9174 T_{3}^{7} + 23882 T_{3}^{6} - 15232 T_{3}^{5} - 17609 T_{3}^{4} + \cdots + 16 \)
T3^17 - 5*T3^16 - 19*T3^15 + 121*T3^14 + 112*T3^13 - 1172*T3^12 - 25*T3^11 + 5845*T3^10 - 2233*T3^9 - 16035*T3^8 + 9174*T3^7 + 23882*T3^6 - 15232*T3^5 - 17609*T3^4 + 10764*T3^3 + 4764*T3^2 - 2368*T3 + 16
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{17} \)
(T + 1)^17
$3$
\( T^{17} - 5 T^{16} - 19 T^{15} + 121 T^{14} + \cdots + 16 \)
T^17 - 5*T^16 - 19*T^15 + 121*T^14 + 112*T^13 - 1172*T^12 - 25*T^11 + 5845*T^10 - 2233*T^9 - 16035*T^8 + 9174*T^7 + 23882*T^6 - 15232*T^5 - 17609*T^4 + 10764*T^3 + 4764*T^2 - 2368*T + 16
$5$
\( T^{17} - 6 T^{16} - 30 T^{15} + 229 T^{14} + \cdots + 59 \)
T^17 - 6*T^16 - 30*T^15 + 229*T^14 + 192*T^13 - 3046*T^12 + 1421*T^11 + 16993*T^10 - 16998*T^9 - 41422*T^8 + 49514*T^7 + 45745*T^6 - 48001*T^5 - 30759*T^4 + 13807*T^3 + 10481*T^2 + 1663*T + 59
$7$
\( T^{17} + 9 T^{16} - 15 T^{15} + \cdots - 70204 \)
T^17 + 9*T^16 - 15*T^15 - 324*T^14 - 266*T^13 + 4501*T^12 + 7438*T^11 - 30665*T^10 - 64622*T^9 + 106176*T^8 + 269571*T^7 - 159681*T^6 - 567397*T^5 + 3166*T^4 + 540254*T^3 + 188531*T^2 - 143448*T - 70204
$11$
\( (T + 1)^{17} \)
(T + 1)^17
$13$
\( T^{17} + 16 T^{16} + 37 T^{15} + \cdots + 4772 \)
T^17 + 16*T^16 + 37*T^15 - 595*T^14 - 3163*T^13 + 3959*T^12 + 52039*T^11 + 46562*T^10 - 293069*T^9 - 585713*T^8 + 324114*T^7 + 1673362*T^6 + 1169252*T^5 - 398432*T^4 - 726102*T^3 - 212635*T^2 + 8230*T + 4772
$17$
\( T^{17} + 8 T^{16} - 102 T^{15} + \cdots - 12481868 \)
T^17 + 8*T^16 - 102*T^15 - 725*T^14 + 5031*T^13 + 25833*T^12 - 151021*T^11 - 419038*T^10 + 2716120*T^9 + 2169813*T^8 - 25608853*T^7 + 13974829*T^6 + 92566830*T^5 - 119075019*T^4 - 54669251*T^3 + 105791123*T^2 + 4643266*T - 12481868
$19$
\( T^{17} + 23 T^{16} + 128 T^{15} + \cdots - 520852 \)
T^17 + 23*T^16 + 128*T^15 - 800*T^14 - 10798*T^13 - 24704*T^12 + 119286*T^11 + 611631*T^10 + 197378*T^9 - 3361505*T^8 - 5543559*T^7 + 3038309*T^6 + 13913858*T^5 + 7983040*T^4 - 6442066*T^3 - 9238945*T^2 - 3768654*T - 520852
$23$
\( T^{17} - 12 T^{16} - 67 T^{15} + \cdots - 11579504 \)
T^17 - 12*T^16 - 67*T^15 + 1270*T^14 - 397*T^13 - 45261*T^12 + 92737*T^11 + 718994*T^10 - 2046030*T^9 - 5711606*T^8 + 18709188*T^7 + 24205564*T^6 - 79508169*T^5 - 60436617*T^4 + 146442434*T^3 + 82573448*T^2 - 69983368*T - 11579504
$29$
\( T^{17} - 196 T^{15} + \cdots + 151663444 \)
T^17 - 196*T^15 - 151*T^14 + 14985*T^13 + 19675*T^12 - 565388*T^11 - 911056*T^10 + 11131961*T^9 + 18300918*T^8 - 114253783*T^7 - 165035536*T^6 + 561171040*T^5 + 616791771*T^4 - 966292817*T^3 - 940827929*T^2 + 236733066*T + 151663444
$31$
\( T^{17} + 8 T^{16} - 214 T^{15} + \cdots - 2634679 \)
T^17 + 8*T^16 - 214*T^15 - 1775*T^14 + 15636*T^13 + 138826*T^12 - 456231*T^11 - 4696997*T^10 + 4562043*T^9 + 70473640*T^8 + 2742844*T^7 - 445822510*T^6 - 181971796*T^5 + 924814030*T^4 + 114207893*T^3 - 534436720*T^2 + 124051126*T - 2634679
$37$
\( T^{17} + 7 T^{16} + \cdots + 1082618944 \)
T^17 + 7*T^16 - 196*T^15 - 1033*T^14 + 16749*T^13 + 51145*T^12 - 786136*T^11 - 648386*T^10 + 20080223*T^9 - 21150491*T^8 - 230708000*T^7 + 610737700*T^6 + 436287179*T^5 - 3196842641*T^4 + 3146274956*T^3 + 1042407932*T^2 - 2880267984*T + 1082618944
$41$
\( T^{17} + 27 T^{16} + \cdots + 504538797980 \)
T^17 + 27*T^16 - 61*T^15 - 7180*T^14 - 33831*T^13 + 672053*T^12 + 5393417*T^11 - 24966825*T^10 - 315354051*T^9 + 169055506*T^8 + 8551716015*T^7 + 11495005671*T^6 - 102528054304*T^5 - 267502559353*T^4 + 314662765099*T^3 + 1635474549455*T^2 + 1670491574722*T + 504538797980
$43$
\( T^{17} + 13 T^{16} + \cdots - 2209597888 \)
T^17 + 13*T^16 - 255*T^15 - 3509*T^14 + 24304*T^13 + 367243*T^12 - 1034252*T^11 - 18709357*T^10 + 16621848*T^9 + 475645678*T^8 + 35397681*T^7 - 5569661316*T^6 - 2026379302*T^5 + 26797010622*T^4 + 3680842307*T^3 - 44727901191*T^2 + 19788616232*T - 2209597888
$47$
\( T^{17} - 23 T^{16} + \cdots - 3671094604336 \)
T^17 - 23*T^16 - 172*T^15 + 7285*T^14 - 9458*T^13 - 883368*T^12 + 4071378*T^11 + 50192853*T^10 - 359743754*T^9 - 1180473831*T^8 + 14228017366*T^7 - 3654072976*T^6 - 248550955991*T^5 + 584482881039*T^4 + 1077674991082*T^3 - 5967783189240*T^2 + 8165111579096*T - 3671094604336
$53$
\( T^{17} - 14 T^{16} + \cdots + 53757717392 \)
T^17 - 14*T^16 - 198*T^15 + 3317*T^14 + 12524*T^13 - 304196*T^12 - 134023*T^11 + 13728095*T^10 - 16105639*T^9 - 316449393*T^8 + 680083870*T^7 + 3414686235*T^6 - 10026117735*T^5 - 12279355111*T^4 + 52886435040*T^3 - 2032270660*T^2 - 90316360704*T + 53757717392
$59$
\( T^{17} - 2 T^{16} + \cdots + 15161840124931 \)
T^17 - 2*T^16 - 546*T^15 + 1282*T^14 + 119356*T^13 - 298454*T^12 - 13480252*T^11 + 32981421*T^10 + 850345493*T^9 - 1827782397*T^8 - 30597930443*T^7 + 48524243432*T^6 + 624074200809*T^5 - 536777278628*T^4 - 6656898722037*T^3 + 826213732032*T^2 + 28581173658371*T + 15161840124931
$61$
\( T^{17} + \cdots - 101563158656816 \)
T^17 + 49*T^16 + 543*T^15 - 9762*T^14 - 238113*T^13 - 244571*T^12 + 28996311*T^11 + 175631730*T^10 - 1359707216*T^9 - 14619494678*T^8 + 13890107151*T^7 + 498419209683*T^6 + 678602681070*T^5 - 7346622934018*T^4 - 16733610763370*T^3 + 42712755688885*T^2 + 90761802775896*T - 101563158656816
$67$
\( T^{17} + 5 T^{16} + \cdots + 564209728960 \)
T^17 + 5*T^16 - 360*T^15 - 1885*T^14 + 51315*T^13 + 267363*T^12 - 3827472*T^11 - 18934187*T^10 + 165023580*T^9 + 733351871*T^8 - 4231691311*T^7 - 15684284171*T^6 + 62615436473*T^5 + 173857467545*T^4 - 475686966096*T^3 - 818452887412*T^2 + 1352100561328*T + 564209728960
$71$
\( T^{17} + 5 T^{16} + \cdots + 44058229429 \)
T^17 + 5*T^16 - 520*T^15 - 3187*T^14 + 96973*T^13 + 673636*T^12 - 8304536*T^11 - 63519877*T^10 + 342504077*T^9 + 2889761486*T^8 - 6334526509*T^7 - 61025997774*T^6 + 41713006537*T^5 + 498679073765*T^4 - 29735197929*T^3 - 553118669814*T^2 + 166205126314*T + 44058229429
$73$
\( T^{17} + 54 T^{16} + \cdots + 4111126564172 \)
T^17 + 54*T^16 + 1003*T^15 + 3430*T^14 - 133800*T^13 - 1844324*T^12 - 3523700*T^11 + 104196737*T^10 + 865226238*T^9 + 669639617*T^8 - 23770908858*T^7 - 125664226769*T^6 - 97460117784*T^5 + 1330960050060*T^4 + 5875686284147*T^3 + 11272334931651*T^2 + 10722738804480*T + 4111126564172
$79$
\( T^{17} + 11 T^{16} + \cdots - 10646788395196 \)
T^17 + 11*T^16 - 809*T^15 - 9594*T^14 + 246825*T^13 + 3287399*T^12 - 34592428*T^11 - 562249600*T^10 + 1935737223*T^9 + 50163725408*T^8 + 25136986901*T^7 - 2154945817103*T^6 - 6587868480325*T^5 + 30256202011216*T^4 + 171451396436587*T^3 + 206778506124357*T^2 + 22554784162546*T - 10646788395196
$83$
\( T^{17} + 8 T^{16} + \cdots - 130397400052 \)
T^17 + 8*T^16 - 479*T^15 - 4562*T^14 + 65041*T^13 + 769378*T^12 - 1740092*T^11 - 40161965*T^10 - 41214719*T^9 + 809403706*T^8 + 2000843557*T^7 - 6411277862*T^6 - 24305898679*T^5 + 11092401330*T^4 + 108085421671*T^3 + 58135736015*T^2 - 140170899894*T - 130397400052
$89$
\( T^{17} + 9 T^{16} + \cdots + 78583924480 \)
T^17 + 9*T^16 - 458*T^15 - 3014*T^14 + 86347*T^13 + 351026*T^12 - 8401081*T^11 - 15790833*T^10 + 436410157*T^9 + 112873030*T^8 - 11458348760*T^7 + 8144307704*T^6 + 131428994398*T^5 - 111464247465*T^4 - 602395302444*T^3 + 236642644736*T^2 + 679264443456*T + 78583924480
$97$
\( T^{17} + 42 T^{16} + \cdots - 97\!\cdots\!65 \)
T^17 + 42*T^16 - 164*T^15 - 26793*T^14 - 159542*T^13 + 6556118*T^12 + 64179355*T^11 - 773199239*T^10 - 9833659366*T^9 + 44921262320*T^8 + 757607891509*T^7 - 1049971575411*T^6 - 30917452306153*T^5 - 8584187056901*T^4 + 633058302721457*T^3 + 805690005114851*T^2 - 5072935608429972*T - 9797952975442865
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