
// Make newform 64.24.b.c in Magma, downloaded from the LMFDB on 03 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_64_b();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_64_24_b_c();".
// 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_64_b();"
function MakeCharacter_64_b()
    N := 64;
    order := 2;
    char_gens := [63, 5];
    v := [2, 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_64_b_Hecke(Kf)
    return MakeCharacter_64_b();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_64_24_b_c();".
// 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_64_24_b_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_64_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,24,sign)));
    Vf := Kernel([<3,R![639853565015953921272403509453868293801980570204062351132961137783204679005764300374016, 0, 227517531085371400339655885692894349473419107765731022881578480302040796495872, 0, 21770934423165115384132640956135061962525331860218333092225492434944, 0, 721708374624256379840316014236033790937311199363019726848, 0, 11284325659321365251912676745228950291388245504, 0, 94460321040967217744454216270509568, 0, 435370496651085702670272, 0, 1039233853600, 0, 1]>],Snew);
    return Vf;
end function;