
// Make newform 105.3.t.b in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_105_t();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_3_t_b();".
// 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_105_t();"
function MakeCharacter_105_t()
    N := 105;
    order := 6;
    char_gens := [71, 22, 31];
    v := [3, 6, 4];
    // 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_105_t_Hecke(Kf)
    return MakeCharacter_105_t();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_3_t_b();".
// 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_105_3_t_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_105_t();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<2,R![22915904400, 0, -102420074880, 0, 286715060416, 0, -486224490072, 0, 594289603224, 0, -511720301004, 0, 329628738209, 0, -153959182710, 0, 54620790105, 0, -14659706670, 0, 3076742670, 0, -507416694, 0, 66770733, 0, -6959778, 0, 573854, 0, -36282, 0, 1713, 0, -54, 0, 1]>],Snew);
    return Vf;
end function;