[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 4);
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
\(3\)
\(1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{10} + T_{2}^{9} - 61 T_{2}^{8} - 54 T_{2}^{7} + 1219 T_{2}^{6} + 1069 T_{2}^{5} - 8923 T_{2}^{4} - 9432 T_{2}^{3} + 18852 T_{2}^{2} + 30528 T_{2} + 10944 \)
T2^10 + T2^9 - 61*T2^8 - 54*T2^7 + 1219*T2^6 + 1069*T2^5 - 8923*T2^4 - 9432*T2^3 + 18852*T2^2 + 30528*T2 + 10944
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\).
$p$
$F_p(T)$
$2$
\( T^{10} + T^{9} - 61 T^{8} - 54 T^{7} + \cdots + 10944 \)
T^10 + T^9 - 61*T^8 - 54*T^7 + 1219*T^6 + 1069*T^5 - 8923*T^4 - 9432*T^3 + 18852*T^2 + 30528*T + 10944
$3$
\( (T + 3)^{10} \)
(T + 3)^10
$5$
\( T^{10} \)
T^10
$7$
\( T^{10} - 51 T^{9} + \cdots - 23688338000 \)
T^10 - 51*T^9 - 714*T^8 + 71509*T^7 - 628694*T^6 - 19439635*T^5 + 336362365*T^4 - 323522140*T^3 - 19847195680*T^2 + 94141338400*T - 23688338000
$11$
\( T^{10} + 36 T^{9} + \cdots + 43932717994176 \)
T^10 + 36*T^9 - 7068*T^8 - 286566*T^7 + 12361783*T^6 + 500303658*T^5 - 7306518036*T^4 - 260805399552*T^3 + 1225585373616*T^2 + 38974543625952*T + 43932717994176
$13$
\( T^{10} - 41 T^{9} + \cdots - 13\!\cdots\!89 \)
T^10 - 41*T^9 - 14978*T^8 + 618701*T^7 + 70660933*T^6 - 2683316668*T^5 - 114661717621*T^4 + 2999941940217*T^3 + 72742261387886*T^2 - 757275428040777*T - 13696419486602789
$17$
\( T^{10} - 70 T^{9} + \cdots - 30\!\cdots\!64 \)
T^10 - 70*T^9 - 19310*T^8 + 1114120*T^7 + 124795445*T^6 - 5146938538*T^5 - 332696006920*T^4 + 8675380077240*T^3 + 296764290258720*T^2 - 5677380770165280*T - 30178122465622464
$19$
\( T^{10} + \cdots - 128742355320975 \)
T^10 + 109*T^9 - 15450*T^8 - 902915*T^7 + 82728155*T^6 + 655989584*T^5 - 77197600349*T^4 + 215135541255*T^3 + 20174848978210*T^2 - 163105325975625*T - 128742355320975
$23$
\( T^{10} + 148 T^{9} + \cdots + 25\!\cdots\!00 \)
T^10 + 148*T^9 - 36421*T^8 - 4614438*T^7 + 442761051*T^6 + 40860064620*T^5 - 2147973943680*T^4 - 68315447021040*T^3 + 4833482626775520*T^2 - 73887397364131200*T + 256953763919678400
$29$
\( T^{10} + 1018 T^{9} + \cdots - 65\!\cdots\!20 \)
T^10 + 1018*T^9 + 353345*T^8 + 33196170*T^7 - 6795812555*T^6 - 1460088588122*T^5 - 20684194621516*T^4 + 9086611217107920*T^3 + 295334031279174000*T^2 - 7042601177142423840*T - 6585603476019174720
$31$
\( T^{10} + 47 T^{9} + \cdots - 85\!\cdots\!25 \)
T^10 + 47*T^9 - 107776*T^8 - 1585137*T^7 + 3887288201*T^6 + 587336620*T^5 - 59633345016345*T^4 + 423815203089925*T^3 + 391737935381625500*T^2 - 3240604726550804375*T - 859782312877367163125
$37$
\( T^{10} - 391 T^{9} + \cdots - 71\!\cdots\!00 \)
T^10 - 391*T^9 - 78884*T^8 + 45796409*T^7 - 1525553344*T^6 - 1052103280275*T^5 + 61784629974415*T^4 + 8142026474017200*T^3 - 344414045355978600*T^2 - 11192422043921922000*T - 71591973561953010000
$41$
\( T^{10} + 492 T^{9} + \cdots + 34\!\cdots\!00 \)
T^10 + 492*T^9 - 173411*T^8 - 101508552*T^7 + 4195250701*T^6 + 5447231903100*T^5 + 320831317553200*T^4 - 35352101862897600*T^3 - 3316529453502842880*T^2 - 65955029598009446400*T + 3453499480567910400
$43$
\( T^{10} - 919 T^{9} + \cdots + 11\!\cdots\!69 \)
T^10 - 919*T^9 + 61343*T^8 + 160798194*T^7 - 42989514283*T^6 - 3092215035149*T^5 + 1866080975851513*T^4 - 104859390616409286*T^3 - 6558966161692975253*T^2 + 320199271685703309521*T + 11902530677310924872069
$47$
\( T^{10} + 88 T^{9} + \cdots + 22\!\cdots\!96 \)
T^10 + 88*T^9 - 745988*T^8 - 48242272*T^7 + 180164662112*T^6 + 11607409881088*T^5 - 15506862098507968*T^4 - 1703673389745107712*T^3 + 393523210066896828672*T^2 + 67504723997212042103808*T + 2290761145633071649591296
$53$
\( T^{10} - 462 T^{9} + \cdots - 47\!\cdots\!00 \)
T^10 - 462*T^9 - 527216*T^8 + 188827752*T^7 + 100149880576*T^6 - 24565536689760*T^5 - 8564582559202880*T^4 + 1054647679976716800*T^3 + 285062893192421329920*T^2 - 1790730460395828633600*T - 475544719027980288000
$59$
\( T^{10} + 596 T^{9} + \cdots - 94\!\cdots\!80 \)
T^10 + 596*T^9 - 791980*T^8 - 645018090*T^7 + 46420166455*T^6 + 156097701681566*T^5 + 49091252653575116*T^4 + 5732876833348248720*T^3 + 140406759826238474880*T^2 - 18309844659092568076800*T - 942579219653368694830080
$61$
\( T^{10} + 1199 T^{9} + \cdots - 20\!\cdots\!61 \)
T^10 + 1199*T^9 - 1092502*T^8 - 1584809019*T^7 + 279632549657*T^6 + 654638422007764*T^5 - 220079288122977*T^4 - 99805152579054995939*T^3 - 1496197264590779760358*T^2 + 5184911616336708672386059*T - 207629824460764890877100861
$67$
\( T^{10} + 405 T^{9} + \cdots - 28\!\cdots\!09 \)
T^10 + 405*T^9 - 1716720*T^8 - 641259475*T^7 + 944665844965*T^6 + 286445478060792*T^5 - 184989079152034945*T^4 - 28241759444482310245*T^3 + 13560489326028829050600*T^2 + 623050356504709808076915*T - 287955158090399277396215509
$71$
\( T^{10} - 540 T^{9} + \cdots - 29\!\cdots\!96 \)
T^10 - 540*T^9 - 721575*T^8 + 335489010*T^7 + 160813440495*T^6 - 67781160174354*T^5 - 13364138317825220*T^4 + 5113338485496140400*T^3 + 337084072005629387280*T^2 - 101364844160034853374240*T - 2967416400809193742639296
$73$
\( T^{10} - 177 T^{9} + \cdots - 82\!\cdots\!00 \)
T^10 - 177*T^9 - 2498456*T^8 + 552104867*T^7 + 2259720113036*T^6 - 547761191337485*T^5 - 880974110161603365*T^4 + 198658630814037978940*T^3 + 139038428631887168721820*T^2 - 18365320086627786643753200*T - 8227358183376616971015795600
$79$
\( T^{10} + 4065 T^{9} + \cdots - 47\!\cdots\!25 \)
T^10 + 4065*T^9 + 6203645*T^8 + 3987572810*T^7 + 303806674465*T^6 - 887764045643725*T^5 - 355842637158819725*T^4 + 8778609137145594450*T^3 + 23010046466218340678775*T^2 + 1091815282298102599643625*T - 476502655003237368121726125
$83$
\( T^{10} + 732 T^{9} + \cdots - 19\!\cdots\!04 \)
T^10 + 732*T^9 - 2178024*T^8 - 1455571902*T^7 + 1318930049599*T^6 + 856021192199778*T^5 - 230071692803515392*T^4 - 163566793680583796856*T^3 + 935821945248183096192*T^2 + 5655233237280790931273376*T - 19079506332283242711559104
$89$
\( T^{10} - 1866 T^{9} + \cdots + 45\!\cdots\!20 \)
T^10 - 1866*T^9 - 2096810*T^8 + 4851782280*T^7 + 902188361725*T^6 - 4186086250439166*T^5 + 402776731781151196*T^4 + 1425750082203833248080*T^3 - 321453788824179845872080*T^2 - 157937928159550855239485280*T + 45811316400564107466105491520
$97$
\( T^{10} - 895 T^{9} + \cdots + 49\!\cdots\!11 \)
T^10 - 895*T^9 - 4610735*T^8 + 4221662970*T^7 + 6144596846045*T^6 - 5560517076068513*T^5 - 2953339684482003145*T^4 + 2710169909145985804590*T^3 + 348521380965371524482295*T^2 - 441292274348529976299914155*T + 49323759625732491775898068411
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