[N,k,chi] = [889,2,Mod(1,889)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(889, 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("889.1");
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
\(7\)
\(1\)
\(127\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{15} - 22 T_{2}^{13} + 186 T_{2}^{11} - 763 T_{2}^{9} + 7 T_{2}^{8} + 1588 T_{2}^{7} - 64 T_{2}^{6} - 1625 T_{2}^{5} + 185 T_{2}^{4} + 726 T_{2}^{3} - 145 T_{2}^{2} - 83 T_{2} + 13 \)
T2^15 - 22*T2^13 + 186*T2^11 - 763*T2^9 + 7*T2^8 + 1588*T2^7 - 64*T2^6 - 1625*T2^5 + 185*T2^4 + 726*T2^3 - 145*T2^2 - 83*T2 + 13
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(889))\).
$p$
$F_p(T)$
$2$
\( T^{15} - 22 T^{13} + 186 T^{11} + \cdots + 13 \)
T^15 - 22*T^13 + 186*T^11 - 763*T^9 + 7*T^8 + 1588*T^7 - 64*T^6 - 1625*T^5 + 185*T^4 + 726*T^3 - 145*T^2 - 83*T + 13
$3$
\( T^{15} - 4 T^{14} - 19 T^{13} + 82 T^{12} + \cdots - 32 \)
T^15 - 4*T^14 - 19*T^13 + 82*T^12 + 137*T^11 - 646*T^10 - 462*T^9 + 2424*T^8 + 698*T^7 - 4343*T^6 - 197*T^5 + 3279*T^4 - 641*T^3 - 776*T^2 + 320*T - 32
$5$
\( T^{15} - 7 T^{14} - 13 T^{13} + \cdots - 2294 \)
T^15 - 7*T^14 - 13*T^13 + 167*T^12 - 42*T^11 - 1477*T^10 + 1357*T^9 + 6009*T^8 - 7622*T^7 - 11384*T^6 + 18028*T^5 + 8499*T^4 - 19249*T^3 + 396*T^2 + 7628*T - 2294
$7$
\( (T + 1)^{15} \)
(T + 1)^15
$11$
\( T^{15} - 14 T^{14} + 2 T^{13} + \cdots - 302112 \)
T^15 - 14*T^14 + 2*T^13 + 743*T^12 - 2345*T^11 - 12380*T^10 + 63092*T^9 + 50769*T^8 - 596721*T^7 + 336541*T^6 + 2002646*T^5 - 1930756*T^4 - 2545671*T^3 + 2325180*T^2 + 1156336*T - 302112
$13$
\( T^{15} - 6 T^{14} - 62 T^{13} + 318 T^{12} + \cdots - 296 \)
T^15 - 6*T^14 - 62*T^13 + 318*T^12 + 1294*T^11 - 4700*T^10 - 11495*T^9 + 25733*T^8 + 45717*T^7 - 54785*T^6 - 70298*T^5 + 43063*T^4 + 31135*T^3 - 6494*T^2 - 3548*T - 296
$17$
\( T^{15} - 10 T^{14} - 48 T^{13} + \cdots + 13032 \)
T^15 - 10*T^14 - 48*T^13 + 605*T^12 + 471*T^11 - 11245*T^10 + 3151*T^9 + 83564*T^8 - 52135*T^7 - 263389*T^6 + 156683*T^5 + 371016*T^4 - 133265*T^3 - 201246*T^2 + 9188*T + 13032
$19$
\( T^{15} - 13 T^{14} - 43 T^{13} + \cdots - 2261282 \)
T^15 - 13*T^14 - 43*T^13 + 1008*T^12 - 87*T^11 - 29691*T^10 + 27952*T^9 + 406142*T^8 - 489036*T^7 - 2526558*T^6 + 3528781*T^5 + 6214108*T^4 - 10412999*T^3 - 2237368*T^2 + 7583414*T - 2261282
$23$
\( T^{15} - 15 T^{14} - 26 T^{13} + \cdots + 159348 \)
T^15 - 15*T^14 - 26*T^13 + 1316*T^12 - 4312*T^11 - 21034*T^10 + 105137*T^9 + 103897*T^8 - 848611*T^7 + 26537*T^6 + 2690496*T^5 - 987376*T^4 - 2726729*T^3 + 347488*T^2 + 938896*T + 159348
$29$
\( T^{15} - 16 T^{14} - 56 T^{13} + \cdots - 24350536 \)
T^15 - 16*T^14 - 56*T^13 + 1882*T^12 - 2886*T^11 - 70623*T^10 + 215665*T^9 + 1061097*T^8 - 4288104*T^7 - 5564005*T^6 + 33033627*T^5 - 3498790*T^4 - 88356051*T^3 + 77370370*T^2 + 14523124*T - 24350536
$31$
\( T^{15} - 22 T^{14} + \cdots - 508362642 \)
T^15 - 22*T^14 + 9*T^13 + 2428*T^12 - 7618*T^11 - 109645*T^10 + 389654*T^9 + 2558037*T^8 - 8374648*T^7 - 31279304*T^6 + 90468548*T^5 + 180867980*T^4 - 492781149*T^3 - 310644668*T^2 + 1106349290*T - 508362642
$37$
\( T^{15} + 14 T^{14} + \cdots - 40940005196 \)
T^15 + 14*T^14 - 267*T^13 - 4504*T^12 + 20006*T^11 + 526954*T^10 + 173338*T^9 - 26692292*T^8 - 69180164*T^7 + 537702802*T^6 + 2025308739*T^5 - 3583743265*T^4 - 15372197233*T^3 + 15390327322*T^2 + 38041799844*T - 40940005196
$41$
\( T^{15} - 19 T^{14} - 83 T^{13} + \cdots + 14583848 \)
T^15 - 19*T^14 - 83*T^13 + 3568*T^12 - 10621*T^11 - 194439*T^10 + 1169333*T^9 + 2798248*T^8 - 33413800*T^7 + 35643900*T^6 + 251299276*T^5 - 658940872*T^4 + 181282831*T^3 + 608078046*T^2 - 230325324*T + 14583848
$43$
\( T^{15} + T^{14} - 315 T^{13} + \cdots + 2881799908 \)
T^15 + T^14 - 315*T^13 - 564*T^12 + 35660*T^11 + 94517*T^10 - 1786407*T^9 - 6247768*T^8 + 39674340*T^7 + 175436696*T^6 - 328092937*T^5 - 2129048098*T^4 - 347835737*T^3 + 8894092804*T^2 + 11534877440*T + 2881799908
$47$
\( T^{15} - 49 T^{14} + \cdots - 127047598350 \)
T^15 - 49*T^14 + 729*T^13 + 1496*T^12 - 139778*T^11 + 959163*T^10 + 6135322*T^9 - 95895638*T^8 + 131885457*T^7 + 2971844939*T^6 - 13764122681*T^5 - 12795824849*T^4 + 214902228235*T^3 - 511021588630*T^2 + 441253093900*T - 127047598350
$53$
\( T^{15} + 28 T^{14} + \cdots + 33403676712 \)
T^15 + 28*T^14 + 98*T^13 - 3654*T^12 - 30801*T^11 + 144203*T^10 + 2139384*T^9 - 184942*T^8 - 64167674*T^7 - 111287168*T^6 + 879489034*T^5 + 2439010519*T^4 - 4772909097*T^3 - 17998952606*T^2 + 4044213460*T + 33403676712
$59$
\( T^{15} - 43 T^{14} + \cdots - 925256454912 \)
T^15 - 43*T^14 + 271*T^13 + 12957*T^12 - 213499*T^11 - 428525*T^10 + 29851558*T^9 - 134739376*T^8 - 1311033540*T^7 + 11599350885*T^6 + 6564059213*T^5 - 292568841906*T^4 + 513121211181*T^3 + 2132023558720*T^2 - 5460769807808*T - 925256454912
$61$
\( T^{15} - 27 T^{14} + \cdots - 26580006408 \)
T^15 - 27*T^14 - 194*T^13 + 11185*T^12 - 50907*T^11 - 1308801*T^10 + 13421572*T^9 + 25970152*T^8 - 901720438*T^7 + 3452592981*T^6 + 11201724862*T^5 - 132830835370*T^4 + 455689385783*T^3 - 730785624978*T^2 + 479550998404*T - 26580006408
$67$
\( T^{15} - 3 T^{14} + \cdots - 38013704592 \)
T^15 - 3*T^14 - 429*T^13 + 109*T^12 + 68381*T^11 + 113483*T^10 - 4778569*T^9 - 11542650*T^8 + 160160270*T^7 + 368786488*T^6 - 2759803053*T^5 - 4424502500*T^4 + 22745354025*T^3 + 15964626160*T^2 - 52550554808*T - 38013704592
$71$
\( T^{15} - 55 T^{14} + \cdots - 23410866384 \)
T^15 - 55*T^14 + 1007*T^13 - 1550*T^12 - 197588*T^11 + 2799023*T^10 - 11363279*T^9 - 67198399*T^8 + 813696536*T^7 - 1944600325*T^6 - 7282488239*T^5 + 39961546592*T^4 - 20510965747*T^3 - 126105696164*T^2 + 110079067960*T - 23410866384
$73$
\( T^{15} + 3 T^{14} + \cdots - 1903703128 \)
T^15 + 3*T^14 - 497*T^13 - 3219*T^12 + 76878*T^11 + 753716*T^10 - 2750277*T^9 - 49181910*T^8 - 78035228*T^7 + 712491550*T^6 + 2222729025*T^5 - 920187182*T^4 - 6274180307*T^3 + 680466986*T^2 + 5336675548*T - 1903703128
$79$
\( T^{15} - 18 T^{14} + \cdots + 1041479699184 \)
T^15 - 18*T^14 - 725*T^13 + 13221*T^12 + 205644*T^11 - 3702641*T^10 - 30472075*T^9 + 503736255*T^8 + 2640020147*T^7 - 34020570543*T^6 - 135218638871*T^5 + 966483954027*T^4 + 3290507206821*T^3 - 4051944308660*T^2 - 1449151677880*T + 1041479699184
$83$
\( T^{15} + \cdots + 328479194135568 \)
T^15 - 17*T^14 - 697*T^13 + 12519*T^12 + 188435*T^11 - 3680554*T^10 - 24822587*T^9 + 556654409*T^8 + 1579912188*T^7 - 46145435712*T^6 - 33913916623*T^5 + 2045732572104*T^4 - 719244096109*T^3 - 43188819334612*T^2 + 26108183669288*T + 328479194135568
$89$
\( T^{15} - 36 T^{14} + \cdots + 217040265526 \)
T^15 - 36*T^14 - 26*T^13 + 12689*T^12 - 60226*T^11 - 1848895*T^10 + 10538659*T^9 + 145635646*T^8 - 721951856*T^7 - 6434440611*T^6 + 22313800962*T^5 + 140628637853*T^4 - 318862132135*T^3 - 1165595467422*T^2 + 1816948721504*T + 217040265526
$97$
\( T^{15} + 2 T^{14} + \cdots - 1094692262 \)
T^15 + 2*T^14 - 539*T^13 - 2081*T^12 + 104362*T^11 + 628152*T^10 - 8012469*T^9 - 73952946*T^8 + 101295113*T^7 + 2955118798*T^6 + 10171027643*T^5 + 3345558804*T^4 - 36602944525*T^3 - 38811049566*T^2 + 20388908342*T - 1094692262
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