[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
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
\(2\)
\(-1\)
\(5\)
\(-1\)
\(601\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{16} + 8 T_{3}^{15} + 9 T_{3}^{14} - 79 T_{3}^{13} - 204 T_{3}^{12} + 206 T_{3}^{11} + 1015 T_{3}^{10} + 71 T_{3}^{9} - 2142 T_{3}^{8} - 864 T_{3}^{7} + 2183 T_{3}^{6} + 979 T_{3}^{5} - 1132 T_{3}^{4} - 370 T_{3}^{3} + 268 T_{3}^{2} + \cdots - 19 \)
T3^16 + 8*T3^15 + 9*T3^14 - 79*T3^13 - 204*T3^12 + 206*T3^11 + 1015*T3^10 + 71*T3^9 - 2142*T3^8 - 864*T3^7 + 2183*T3^6 + 979*T3^5 - 1132*T3^4 - 370*T3^3 + 268*T3^2 + 38*T3 - 19
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{16} \)
(T - 1)^16
$3$
\( T^{16} + 8 T^{15} + 9 T^{14} - 79 T^{13} + \cdots - 19 \)
T^16 + 8*T^15 + 9*T^14 - 79*T^13 - 204*T^12 + 206*T^11 + 1015*T^10 + 71*T^9 - 2142*T^8 - 864*T^7 + 2183*T^6 + 979*T^5 - 1132*T^4 - 370*T^3 + 268*T^2 + 38*T - 19
$5$
\( (T - 1)^{16} \)
(T - 1)^16
$7$
\( T^{16} + 10 T^{15} + 6 T^{14} - 244 T^{13} + \cdots - 104 \)
T^16 + 10*T^15 + 6*T^14 - 244*T^13 - 778*T^12 + 999*T^11 + 7724*T^10 + 6120*T^9 - 21759*T^8 - 41136*T^7 - 322*T^6 + 52697*T^5 + 45005*T^4 + 9704*T^3 - 2939*T^2 - 1309*T - 104
$11$
\( T^{16} + 14 T^{15} + 30 T^{14} + \cdots - 1810 \)
T^16 + 14*T^15 + 30*T^14 - 420*T^13 - 2420*T^12 - 707*T^11 + 25947*T^10 + 69022*T^9 + 15130*T^8 - 190524*T^7 - 297819*T^6 - 116489*T^5 + 83983*T^4 + 76240*T^3 + 5746*T^2 - 8349*T - 1810
$13$
\( T^{16} + 20 T^{15} + 105 T^{14} + \cdots - 131590 \)
T^16 + 20*T^15 + 105*T^14 - 394*T^13 - 5526*T^12 - 11426*T^11 + 55634*T^10 + 274005*T^9 + 164883*T^8 - 1067993*T^7 - 1789965*T^6 + 970741*T^5 + 3751273*T^4 + 1108302*T^3 - 2315944*T^2 - 1546693*T - 131590
$17$
\( T^{16} + 27 T^{15} + \cdots - 123709702 \)
T^16 + 27*T^15 + 228*T^14 - 136*T^13 - 13063*T^12 - 63724*T^11 + 71483*T^10 + 1433036*T^9 + 2847090*T^8 - 8896628*T^7 - 38840511*T^6 - 4194703*T^5 + 169375639*T^4 + 189150829*T^3 - 214428722*T^2 - 425375043*T - 123709702
$19$
\( T^{16} + 17 T^{15} + 23 T^{14} + \cdots + 152506 \)
T^16 + 17*T^15 + 23*T^14 - 1181*T^13 - 8017*T^12 - 4683*T^11 + 113688*T^10 + 325151*T^9 - 178485*T^8 - 1632674*T^7 - 830470*T^6 + 2802585*T^5 + 2045614*T^4 - 2114586*T^3 - 1307451*T^2 + 664301*T + 152506
$23$
\( T^{16} + 9 T^{15} - 131 T^{14} + \cdots + 1723900 \)
T^16 + 9*T^15 - 131*T^14 - 1437*T^13 + 3875*T^12 + 73860*T^11 + 70245*T^10 - 1377950*T^9 - 3988556*T^8 + 5475513*T^7 + 36014640*T^6 + 35988445*T^5 - 39723276*T^4 - 89231396*T^3 - 37054176*T^2 + 7276165*T + 1723900
$29$
\( T^{16} + 23 T^{15} + 25 T^{14} + \cdots + 19604501 \)
T^16 + 23*T^15 + 25*T^14 - 2900*T^13 - 17474*T^12 + 92832*T^11 + 963161*T^10 + 177295*T^9 - 14814007*T^8 - 22142152*T^7 + 71657280*T^6 + 162316129*T^5 - 31453922*T^4 - 221785053*T^3 - 70071316*T^2 + 49581303*T + 19604501
$31$
\( T^{16} + 21 T^{15} + \cdots - 331425593 \)
T^16 + 21*T^15 - 11*T^14 - 2543*T^13 - 7835*T^12 + 112435*T^11 + 465895*T^10 - 2239492*T^9 - 10655875*T^8 + 19550835*T^7 + 110670916*T^6 - 52759875*T^5 - 493707659*T^4 - 71687144*T^3 + 770535592*T^2 + 199936786*T - 331425593
$37$
\( T^{16} + 16 T^{15} + \cdots + 400525795984 \)
T^16 + 16*T^15 - 211*T^14 - 4380*T^13 + 11655*T^12 + 471475*T^11 + 457245*T^10 - 24973674*T^9 - 75413163*T^8 + 646110662*T^7 + 3122063593*T^6 - 5904336736*T^5 - 52930292308*T^4 - 39070915457*T^3 + 274993578476*T^2 + 632800270993*T + 400525795984
$41$
\( T^{16} + 35 T^{15} + \cdots + 1159200242 \)
T^16 + 35*T^15 + 262*T^14 - 4572*T^13 - 86214*T^12 - 277973*T^11 + 3971808*T^10 + 38630310*T^9 + 89331236*T^8 - 297062510*T^7 - 1602575101*T^6 - 461481183*T^5 + 6766836168*T^4 + 5411287873*T^3 - 7846595458*T^2 - 2125986311*T + 1159200242
$43$
\( T^{16} - 3 T^{15} + \cdots + 12020031088 \)
T^16 - 3*T^15 - 334*T^14 + 822*T^13 + 43432*T^12 - 88547*T^11 - 2759996*T^10 + 5011489*T^9 + 88682128*T^8 - 165514776*T^7 - 1369175861*T^6 + 2834583866*T^5 + 8274014295*T^4 - 18374951508*T^3 - 11819483833*T^2 + 22098246473*T + 12020031088
$47$
\( T^{16} + 25 T^{15} + \cdots - 233890112 \)
T^16 + 25*T^15 + 74*T^14 - 2734*T^13 - 22086*T^12 + 59048*T^11 + 1126590*T^10 + 1997113*T^9 - 17101511*T^8 - 73314121*T^7 - 10130641*T^6 + 425009249*T^5 + 726612937*T^4 - 73947252*T^3 - 1154853098*T^2 - 968063801*T - 233890112
$53$
\( T^{16} + 39 T^{15} + \cdots - 527055664361 \)
T^16 + 39*T^15 + 383*T^14 - 3525*T^13 - 86994*T^12 - 297626*T^11 + 4329229*T^10 + 37083012*T^9 - 11129018*T^8 - 1138584787*T^7 - 3477453343*T^6 + 8911901435*T^5 + 65659084407*T^4 + 72163259255*T^3 - 249175226133*T^2 - 714700654822*T - 527055664361
$59$
\( T^{16} + 32 T^{15} + \cdots + 1424918763584 \)
T^16 + 32*T^15 + 39*T^14 - 8780*T^13 - 83399*T^12 + 536324*T^11 + 10258006*T^10 + 11141061*T^9 - 431155131*T^8 - 1675096117*T^7 + 6133621465*T^6 + 41634138445*T^5 - 1602805929*T^4 - 349531035814*T^3 - 393865816149*T^2 + 878818558107*T + 1424918763584
$61$
\( T^{16} + 38 T^{15} + \cdots - 19460885020 \)
T^16 + 38*T^15 + 319*T^14 - 4759*T^13 - 92476*T^12 - 216826*T^11 + 5217573*T^10 + 39729348*T^9 + 11177070*T^8 - 858732410*T^7 - 2944892879*T^6 + 645305842*T^5 + 18568932939*T^4 + 22505489121*T^3 - 22969542973*T^2 - 52712451351*T - 19460885020
$67$
\( T^{16} - 5 T^{15} + \cdots + 5064340186319 \)
T^16 - 5*T^15 - 670*T^14 + 3423*T^13 + 164130*T^12 - 793951*T^11 - 18926072*T^10 + 73339650*T^9 + 1181888336*T^8 - 2912844213*T^7 - 40901441444*T^6 + 39431179734*T^5 + 713528328944*T^4 + 177466432609*T^3 - 4651230854263*T^2 - 3531909188020*T + 5064340186319
$71$
\( T^{16} + 16 T^{15} + \cdots + 14387146030835 \)
T^16 + 16*T^15 - 610*T^14 - 10112*T^13 + 138467*T^12 + 2431540*T^11 - 14943075*T^10 - 287661582*T^9 + 777362063*T^8 + 17646780624*T^7 - 15793157470*T^6 - 530335648239*T^5 + 3454667152*T^4 + 6470435002542*T^3 - 251909311907*T^2 - 27676300309077*T + 14387146030835
$73$
\( T^{16} + 17 T^{15} + \cdots - 98804247364918 \)
T^16 + 17*T^15 - 612*T^14 - 11534*T^13 + 130856*T^12 + 2999829*T^11 - 10213169*T^10 - 376532693*T^9 - 103767137*T^8 + 23713059911*T^7 + 51349472653*T^6 - 719541910066*T^5 - 2246132212562*T^4 + 9062416643020*T^3 + 30257925855010*T^2 - 38230038008457*T - 98804247364918
$79$
\( T^{16} + 40 T^{15} + \cdots + 1084834349107 \)
T^16 + 40*T^15 + 150*T^14 - 13004*T^13 - 152700*T^12 + 1231226*T^11 + 25893430*T^10 - 1942379*T^9 - 1774610798*T^8 - 5043040561*T^7 + 51773335570*T^6 + 222132247660*T^5 - 567501861001*T^4 - 2981885884603*T^3 + 1899519250142*T^2 + 12137461333710*T + 1084834349107
$83$
\( T^{16} + 22 T^{15} + \cdots - 4218579966400 \)
T^16 + 22*T^15 - 575*T^14 - 13813*T^13 + 125985*T^12 + 3364262*T^11 - 13901157*T^10 - 406008845*T^9 + 916030138*T^8 + 25396810987*T^7 - 44570244003*T^6 - 766087232683*T^5 + 1570782079794*T^4 + 8090584434756*T^3 - 22977280999592*T^2 + 17828118802000*T - 4218579966400
$89$
\( T^{16} + 46 T^{15} + \cdots - 1877257307863 \)
T^16 + 46*T^15 + 435*T^14 - 10566*T^13 - 233914*T^12 - 419435*T^11 + 24350781*T^10 + 181835236*T^9 - 545754098*T^8 - 9244115192*T^7 - 7327843542*T^6 + 174778052522*T^5 + 284607825421*T^4 - 1419603122721*T^3 - 1359936221674*T^2 + 4992764652805*T - 1877257307863
$97$
\( T^{16} + \cdots + 239291495389240 \)
T^16 + 21*T^15 - 734*T^14 - 17535*T^13 + 182323*T^12 + 5635840*T^11 - 13368029*T^10 - 877819398*T^9 - 1384724780*T^8 + 67925578777*T^7 + 275061505163*T^6 - 2310014611432*T^5 - 14832495984040*T^4 + 14199404786800*T^3 + 254643330515360*T^2 + 522136692655047*T + 239291495389240
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