[N,k,chi] = [1503,2,Mod(1,1503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1503, 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("1503.1");
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
\(3\)
\(1\)
\(167\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{14} + 6 T_{2}^{13} - 4 T_{2}^{12} - 82 T_{2}^{11} - 72 T_{2}^{10} + 394 T_{2}^{9} + 586 T_{2}^{8} - 766 T_{2}^{7} - 1589 T_{2}^{6} + 364 T_{2}^{5} + 1665 T_{2}^{4} + 406 T_{2}^{3} - 440 T_{2}^{2} - 162 T_{2} + 9 \)
T2^14 + 6*T2^13 - 4*T2^12 - 82*T2^11 - 72*T2^10 + 394*T2^9 + 586*T2^8 - 766*T2^7 - 1589*T2^6 + 364*T2^5 + 1665*T2^4 + 406*T2^3 - 440*T2^2 - 162*T2 + 9
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\).
$p$
$F_p(T)$
$2$
\( T^{14} + 6 T^{13} - 4 T^{12} - 82 T^{11} + \cdots + 9 \)
T^14 + 6*T^13 - 4*T^12 - 82*T^11 - 72*T^10 + 394*T^9 + 586*T^8 - 766*T^7 - 1589*T^6 + 364*T^5 + 1665*T^4 + 406*T^3 - 440*T^2 - 162*T + 9
$3$
\( T^{14} \)
T^14
$5$
\( T^{14} + 12 T^{13} + 31 T^{12} + \cdots + 9738 \)
T^14 + 12*T^13 + 31*T^12 - 140*T^11 - 705*T^10 + 214*T^9 + 4664*T^8 + 2078*T^7 - 15073*T^6 - 9186*T^5 + 26865*T^4 + 13588*T^3 - 25468*T^2 - 6666*T + 9738
$7$
\( T^{14} - 46 T^{12} - 6 T^{11} + \cdots - 2016 \)
T^14 - 46*T^12 - 6*T^11 + 799*T^10 + 140*T^9 - 6509*T^8 - 852*T^7 + 25331*T^6 + 1070*T^5 - 42903*T^4 - 2200*T^3 + 26728*T^2 + 3792*T - 2016
$11$
\( T^{14} + 12 T^{13} - 17 T^{12} + \cdots + 134172 \)
T^14 + 12*T^13 - 17*T^12 - 792*T^11 - 2879*T^10 + 9100*T^9 + 84252*T^8 + 167572*T^7 - 169961*T^6 - 1215736*T^5 - 1912385*T^4 - 1045816*T^3 + 262004*T^2 + 481596*T + 134172
$13$
\( T^{14} + 2 T^{13} - 90 T^{12} + \cdots - 1173488 \)
T^14 + 2*T^13 - 90*T^12 - 160*T^11 + 2987*T^10 + 5314*T^9 - 47554*T^8 - 87892*T^7 + 378774*T^6 + 725300*T^5 - 1378479*T^4 - 2623536*T^3 + 1706744*T^2 + 2450544*T - 1173488
$17$
\( T^{14} + 26 T^{13} + 229 T^{12} + \cdots - 63758 \)
T^14 + 26*T^13 + 229*T^12 + 494*T^11 - 3626*T^10 - 18362*T^9 + 7452*T^8 + 161868*T^7 + 118837*T^6 - 563874*T^5 - 671187*T^4 + 659686*T^3 + 1013332*T^2 + 87298*T - 63758
$19$
\( T^{14} - 158 T^{12} + 100 T^{11} + \cdots + 99136 \)
T^14 - 158*T^12 + 100*T^11 + 9337*T^10 - 10418*T^9 - 251924*T^8 + 360426*T^7 + 2971884*T^6 - 4508128*T^5 - 10959831*T^4 + 11183076*T^3 + 2979136*T^2 - 1464128*T + 99136
$23$
\( T^{14} + 24 T^{13} + 73 T^{12} + \cdots - 98889856 \)
T^14 + 24*T^13 + 73*T^12 - 2746*T^11 - 28345*T^10 - 12232*T^9 + 1237296*T^8 + 7259136*T^7 + 8630897*T^6 - 70707520*T^5 - 358896065*T^4 - 763289388*T^3 - 845858320*T^2 - 466376576*T - 98889856
$29$
\( T^{14} + 16 T^{13} + \cdots + 1671719168 \)
T^14 + 16*T^13 - 155*T^12 - 3444*T^11 + 3723*T^10 + 268364*T^9 + 448458*T^8 - 9276388*T^7 - 28004513*T^6 + 133103528*T^5 + 513867895*T^4 - 508908424*T^3 - 2290249600*T^2 + 944561152*T + 1671719168
$31$
\( T^{14} - 8 T^{13} - 132 T^{12} + \cdots + 22208 \)
T^14 - 8*T^13 - 132*T^12 + 1046*T^11 + 5624*T^10 - 44886*T^9 - 84787*T^8 + 719360*T^7 + 289998*T^6 - 3658644*T^5 + 1029345*T^4 + 5789016*T^3 - 3642128*T^2 - 597024*T + 22208
$37$
\( T^{14} + 8 T^{13} - 151 T^{12} + \cdots - 117862128 \)
T^14 + 8*T^13 - 151*T^12 - 1210*T^11 + 6971*T^10 + 54566*T^9 - 159336*T^8 - 1094470*T^7 + 2094015*T^6 + 10836388*T^5 - 16293967*T^4 - 51566828*T^3 + 68646424*T^2 + 93722688*T - 117862128
$41$
\( T^{14} + 26 T^{13} + 174 T^{12} + \cdots - 3901654 \)
T^14 + 26*T^13 + 174*T^12 - 848*T^11 - 14070*T^10 - 26036*T^9 + 276575*T^8 + 1137220*T^7 - 1128828*T^6 - 10005504*T^5 - 821599*T^4 + 34886388*T^3 + 6123974*T^2 - 40530922*T - 3901654
$43$
\( T^{14} + 6 T^{13} - 320 T^{12} + \cdots - 53183522 \)
T^14 + 6*T^13 - 320*T^12 - 1694*T^11 + 35392*T^10 + 150670*T^9 - 1704309*T^8 - 5512474*T^7 + 34371404*T^6 + 91882284*T^5 - 251938077*T^4 - 610853410*T^3 + 378250558*T^2 + 863659594*T - 53183522
$47$
\( T^{14} + 24 T^{13} + \cdots + 4526879868 \)
T^14 + 24*T^13 - 183*T^12 - 8020*T^11 - 17393*T^10 + 859340*T^9 + 5258423*T^8 - 28047336*T^7 - 325646630*T^6 - 429170412*T^5 + 4972067763*T^4 + 24253835872*T^3 + 44236777664*T^2 + 32207483748*T + 4526879868
$53$
\( T^{14} + 38 T^{13} + \cdots + 23847186266 \)
T^14 + 38*T^13 + 359*T^12 - 3576*T^11 - 84617*T^10 - 297184*T^9 + 4024237*T^8 + 37132240*T^7 + 31550670*T^6 - 807160102*T^5 - 3284933759*T^4 + 171701092*T^3 + 25372203498*T^2 + 49209856490*T + 23847186266
$59$
\( T^{14} + 10 T^{13} + \cdots + 1587058016 \)
T^14 + 10*T^13 - 283*T^12 - 3470*T^11 + 19007*T^10 + 350558*T^9 + 186461*T^8 - 11656478*T^7 - 32220442*T^6 + 112870200*T^5 + 481964159*T^4 - 154681740*T^3 - 1923361592*T^2 - 705995920*T + 1587058016
$61$
\( T^{14} + 4 T^{13} + \cdots + 50051772108 \)
T^14 + 4*T^13 - 442*T^12 - 2428*T^11 + 70429*T^10 + 500862*T^9 - 4634496*T^8 - 44247418*T^7 + 83744996*T^6 + 1629428056*T^5 + 2306473621*T^4 - 18800396204*T^3 - 63984489592*T^2 - 34712683620*T + 50051772108
$67$
\( T^{14} + 6 T^{13} + \cdots + 1972020262 \)
T^14 + 6*T^13 - 440*T^12 - 1430*T^11 + 65889*T^10 + 67330*T^9 - 3746096*T^8 - 2622062*T^7 + 92843760*T^6 + 108258208*T^5 - 900742163*T^4 - 1807176948*T^3 + 1147445254*T^2 + 4219256706*T + 1972020262
$71$
\( T^{14} + 32 T^{13} + \cdots - 2117939328 \)
T^14 + 32*T^13 + 227*T^12 - 3280*T^11 - 60516*T^10 - 228298*T^9 + 1929553*T^8 + 21850992*T^7 + 65043563*T^6 - 142324322*T^5 - 1640826685*T^4 - 5299025404*T^3 - 8580888976*T^2 - 6910289280*T - 2117939328
$73$
\( T^{14} - 494 T^{12} + \cdots + 36765383984 \)
T^14 - 494*T^12 - 206*T^11 + 85267*T^10 + 38146*T^9 - 6386720*T^8 + 253342*T^7 + 222052778*T^6 - 196189310*T^5 - 3556431475*T^4 + 6464460644*T^3 + 19206898384*T^2 - 58053392240*T + 36765383984
$79$
\( T^{14} + 28 T^{13} - 180 T^{12} + \cdots + 54980982 \)
T^14 + 28*T^13 - 180*T^12 - 9270*T^11 + 1944*T^10 + 1167846*T^9 + 1032243*T^8 - 64881660*T^7 - 50539428*T^6 + 1279051376*T^5 + 1114091139*T^4 - 2163759324*T^3 - 634895426*T^2 + 207126246*T + 54980982
$83$
\( T^{14} + 10 T^{13} + \cdots + 3870696730016 \)
T^14 + 10*T^13 - 759*T^12 - 8760*T^11 + 211175*T^10 + 2847870*T^9 - 25525263*T^8 - 437127734*T^7 + 1002387822*T^6 + 32178754122*T^5 + 40741326227*T^4 - 930161460176*T^3 - 3136922906464*T^2 + 1193129962576*T + 3870696730016
$89$
\( T^{14} + 44 T^{13} + \cdots + 194929231744 \)
T^14 + 44*T^13 + 426*T^12 - 7164*T^11 - 146687*T^10 - 64208*T^9 + 13149098*T^8 + 56448008*T^7 - 433246170*T^6 - 2778662448*T^5 + 4636664087*T^4 + 40278606340*T^3 - 28548387840*T^2 - 179790844224*T + 194929231744
$97$
\( T^{14} + 2 T^{13} + \cdots + 36017758368 \)
T^14 + 2*T^13 - 515*T^12 - 1318*T^11 + 103528*T^10 + 293852*T^9 - 10442709*T^8 - 30067750*T^7 + 559710759*T^6 + 1513701418*T^5 - 15160633699*T^4 - 35175509888*T^3 + 161888014288*T^2 + 280005423792*T + 36017758368
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