
// Make newform 755.2.f.d in Magma, downloaded from the LMFDB on 09 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_755_f();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_755_2_f_d();".
// 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_755_f();"
function MakeCharacter_755_f()
    N := 755;
    order := 4;
    char_gens := [152, 6];
    v := [1, 2];
    // 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_755_f_Hecke( : Kf := Kf)
    return MakeCharacter_755_f();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_755_2_f_d();".
// 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_755_2_f_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_755_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![11025, 223440, 2264192, 6896848, 11151616, 6617548, 1132096, 1664362, 9481696, 3217536, 60648, -655424, 2991352, 119168, 722, -42560, 269696, -1064, 0, -532, 10192, -38, 0, 0, 168, 0, 0, 0, 1]>,<3,R![0, 1]>],Snew);
    return Vf;
end function;