
// Make newform 961.6.a.l in Magma, downloaded from the LMFDB on 14 June 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_961_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_961_6_a_l();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_961_a();"
function MakeCharacter_961_a()
    N := 961;
    order := 1;
    char_gens := [3];
    v := [1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_961_a_Hecke( : Kf := Kf)
    return MakeCharacter_961_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_961_6_a_l();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_961_6_a_l( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_961_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,6,sign)));
    Vf := Kernel([<2,R![-176432039292633088, -705798414404026368, 4054569327156658176, 4633323315642564608, -752400461149745152, -1738901917872021504, 5471788510220288, 288080355548274688, 6590873806915584, -27091129810107392, -437430998753024, 1583546209319040, 2693386681424, -60339488651712, 775609807232, 1536510680808, -39226591201, -26306932852, 949132602, 298519614, -13355359, -2149392, 111413, 8878, -512, -16, 1]>,<3,R![25354631883428686190811555705070472670614798282740727808, 0, -140472517947135087914940509258128572639343786549070266368, 0, 61688184833911449672602387694027073338314444328910454784, 0, -11637638234483273264327621193299073336025512072135573504, 0, 1218576410495868078578972095864598295825394446802354176, 0, -79396787864260976183491076361167745126037626580893696, 0, 3455376405577921951290893687167092245738749929603072, 0, -105575639318217442077362090880516329339839465193472, 0, 2349727198721895709518864630852162206283925524480, 0, -39175319512117299998254236771098171141668306944, 0, 499918049466308843425433151590021101335763200, 0, -4964639138344280552549080564593263472496128, 0, 38859510257109720065398931050280706039680, 0, -242022666844311571358737150641094726912, 0, 1207553817545035002735833050650997824, 0, -4847654965978749840580457080855296, 0, 15689574235511398922300936563520, 0, -40926609083706575913644413952, 0, 85794665151635935848684896, 0, -143680353828007468683520, 0, 190348916227955668112, 0, -196483915082608224, 0, 154408423260132, 0, -89097940744, 0, 35543006, 0, -8748, 0, 1]>],Snew);
    return Vf;
end function;