[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6039.1");
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
\(3\)
\(-1\)
\(11\)
\(-1\)
\(61\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{11} - 4 T_{2}^{10} - 6 T_{2}^{9} + 37 T_{2}^{8} - 2 T_{2}^{7} - 109 T_{2}^{6} + 55 T_{2}^{5} + 115 T_{2}^{4} - 76 T_{2}^{3} - 29 T_{2}^{2} + 14 T_{2} + 3 \)
T2^11 - 4*T2^10 - 6*T2^9 + 37*T2^8 - 2*T2^7 - 109*T2^6 + 55*T2^5 + 115*T2^4 - 76*T2^3 - 29*T2^2 + 14*T2 + 3
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\).
$p$
$F_p(T)$
$2$
\( T^{11} - 4 T^{10} - 6 T^{9} + 37 T^{8} + \cdots + 3 \)
T^11 - 4*T^10 - 6*T^9 + 37*T^8 - 2*T^7 - 109*T^6 + 55*T^5 + 115*T^4 - 76*T^3 - 29*T^2 + 14*T + 3
$3$
\( T^{11} \)
T^11
$5$
\( T^{11} - 13 T^{10} + 55 T^{9} - 42 T^{8} + \cdots + 39 \)
T^11 - 13*T^10 + 55*T^9 - 42*T^8 - 276*T^7 + 593*T^6 + 80*T^5 - 997*T^4 + 541*T^3 + 241*T^2 - 233*T + 39
$7$
\( T^{11} + 5 T^{10} - 25 T^{9} - 137 T^{8} + \cdots + 1 \)
T^11 + 5*T^10 - 25*T^9 - 137*T^8 + 117*T^7 + 832*T^6 - 84*T^5 - 789*T^4 + 68*T^3 + 168*T^2 - 36*T + 1
$11$
\( (T - 1)^{11} \)
(T - 1)^11
$13$
\( T^{11} + 3 T^{10} - 65 T^{9} + \cdots - 113383 \)
T^11 + 3*T^10 - 65*T^9 - 241*T^8 + 1159*T^7 + 4961*T^6 - 7470*T^5 - 39255*T^4 + 14930*T^3 + 123422*T^2 + 3351*T - 113383
$17$
\( T^{11} - 7 T^{10} - 55 T^{9} + \cdots - 21027 \)
T^11 - 7*T^10 - 55*T^9 + 414*T^8 + 550*T^7 - 6216*T^6 + 1480*T^5 + 31717*T^4 - 29345*T^3 - 43467*T^2 + 65792*T - 21027
$19$
\( T^{11} + 8 T^{10} - 75 T^{9} + \cdots + 10163 \)
T^11 + 8*T^10 - 75*T^9 - 808*T^8 - 110*T^7 + 18054*T^6 + 58777*T^5 + 40636*T^4 - 65067*T^3 - 65256*T^2 + 23440*T + 10163
$23$
\( T^{11} - 15 T^{10} - 28 T^{9} + \cdots + 198891 \)
T^11 - 15*T^10 - 28*T^9 + 1294*T^8 - 3829*T^7 - 19021*T^6 + 68324*T^5 + 125349*T^4 - 324162*T^3 - 402790*T^2 + 293965*T + 198891
$29$
\( T^{11} - 8 T^{10} - 138 T^{9} + \cdots + 529149 \)
T^11 - 8*T^10 - 138*T^9 + 1304*T^8 + 3752*T^7 - 54383*T^6 + 39283*T^5 + 546735*T^4 - 790222*T^3 - 1579672*T^2 + 2432266*T + 529149
$31$
\( T^{11} + 17 T^{10} - 31 T^{9} + \cdots - 2875241 \)
T^11 + 17*T^10 - 31*T^9 - 2052*T^8 - 10978*T^7 + 17020*T^6 + 292265*T^5 + 624332*T^4 - 1061686*T^3 - 5692731*T^2 - 7151805*T - 2875241
$37$
\( T^{11} + 10 T^{10} - 200 T^{9} + \cdots - 7025731 \)
T^11 + 10*T^10 - 200*T^9 - 2367*T^8 + 8135*T^7 + 153997*T^6 + 192387*T^5 - 2250234*T^4 - 5095379*T^3 + 6369655*T^2 + 13545429*T - 7025731
$41$
\( T^{11} - 25 T^{10} + \cdots + 793812771 \)
T^11 - 25*T^10 - 7*T^9 + 4956*T^8 - 36076*T^7 - 195649*T^6 + 3227590*T^5 - 8038701*T^4 - 56332527*T^3 + 402888285*T^2 - 947582937*T + 793812771
$43$
\( T^{11} + 7 T^{10} - 216 T^{9} + \cdots - 2670529 \)
T^11 + 7*T^10 - 216*T^9 - 1308*T^8 + 13955*T^7 + 69538*T^6 - 262278*T^5 - 1270169*T^4 + 250965*T^3 + 3495471*T^2 + 192860*T - 2670529
$47$
\( T^{11} - 30 T^{10} + \cdots - 149717619 \)
T^11 - 30*T^10 + 143*T^9 + 3624*T^8 - 39030*T^7 - 59993*T^6 + 2218970*T^5 - 6038580*T^4 - 33349623*T^3 + 189644004*T^2 - 209095254*T - 149717619
$53$
\( T^{11} - 18 T^{10} - 122 T^{9} + \cdots - 4627299 \)
T^11 - 18*T^10 - 122*T^9 + 3429*T^8 - 5701*T^7 - 145490*T^6 + 622490*T^5 + 630270*T^4 - 5491619*T^3 + 1318923*T^2 + 11853739*T - 4627299
$59$
\( T^{11} - 43 T^{10} + 589 T^{9} + \cdots + 91481937 \)
T^11 - 43*T^10 + 589*T^9 + T^8 - 79856*T^7 + 846152*T^6 - 3468495*T^5 + 1831155*T^4 + 28924390*T^3 - 72518475*T^2 + 7716625*T + 91481937
$61$
\( (T - 1)^{11} \)
(T - 1)^11
$67$
\( T^{11} + 30 T^{10} + 95 T^{9} + \cdots + 1573457 \)
T^11 + 30*T^10 + 95*T^9 - 3661*T^8 - 18319*T^7 + 167797*T^6 + 671157*T^5 - 3396140*T^4 - 6539939*T^3 + 18825291*T^2 + 16842288*T + 1573457
$71$
\( T^{11} - 7 T^{10} + \cdots + 28070149767 \)
T^11 - 7*T^10 - 642*T^9 + 4276*T^8 + 153392*T^7 - 948191*T^6 - 16655969*T^5 + 90399937*T^4 + 795170142*T^3 - 3297230737*T^2 - 13188415450*T + 28070149767
$73$
\( T^{11} - 6 T^{10} - 489 T^{9} + \cdots + 126285977 \)
T^11 - 6*T^10 - 489*T^9 + 3234*T^8 + 73209*T^7 - 507368*T^6 - 3467923*T^5 + 25723055*T^4 + 13554336*T^3 - 298195786*T^2 + 382533079*T + 126285977
$79$
\( T^{11} - 17 T^{10} - 359 T^{9} + \cdots - 15718043 \)
T^11 - 17*T^10 - 359*T^9 + 5440*T^8 + 51442*T^7 - 565056*T^6 - 3414043*T^5 + 20616376*T^4 + 76623241*T^3 - 224593698*T^2 - 124024133*T - 15718043
$83$
\( T^{11} - 34 T^{10} + \cdots - 18319432683 \)
T^11 - 34*T^10 + 47*T^9 + 9954*T^8 - 91065*T^7 - 761206*T^6 + 12364025*T^5 - 3360632*T^4 - 509253177*T^3 + 1413906330*T^2 + 5286212197*T - 18319432683
$89$
\( T^{11} - 41 T^{10} + \cdots + 78347255019 \)
T^11 - 41*T^10 + 121*T^9 + 16219*T^8 - 215889*T^7 - 1223088*T^6 + 40161014*T^5 - 171004839*T^4 - 1629031162*T^3 + 18409772546*T^2 - 64705237192*T + 78347255019
$97$
\( T^{11} + 41 T^{10} + \cdots - 7174782977 \)
T^11 + 41*T^10 + 293*T^9 - 8855*T^8 - 149502*T^7 - 22406*T^6 + 13934859*T^5 + 84495825*T^4 - 168903364*T^3 - 3117049638*T^2 - 9438663108*T - 7174782977
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