
// Make newform 403.2.f.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_403_f();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_403_2_f_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_403_f();"
function MakeCharacter_403_f()
    N := 403;
    order := 3;
    char_gens := [249, 313];
    v := [1, 3];
    // 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_403_f_Hecke(Kf)
    return MakeCharacter_403_f();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_403_2_f_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_403_2_f_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_403_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![9, 99, 1527, 3624, 55312, -50460, 2336119, -4438295, 23473298, 712721, 55581903, 18793089, 86304279, 41351645, 91389792, 47365752, 71500199, 37043823, 42152394, 20705963, 19086698, 8731825, 6716441, 2798593, 1839299, 692637, 393061, 131199, 64485, 18798, 7983, 1951, 700, 135, 40, 5, 1]>],Snew);
    return Vf;
end function;