
// Make newform 900.3.p.f in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_900_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_900_3_p_f();".
// 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_900_p();"
function MakeCharacter_900_p()
    N := 900;
    order := 6;
    char_gens := [451, 101, 577];
    v := [6, 1, 6];
    // 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_900_p_Hecke(Kf)
    return MakeCharacter_900_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_900_3_p_f();".
// 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_900_3_p_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_900_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<7,R![4469486461456, 0, 18411430333728, 0, 55727495557356, 0, 76951314990680, 0, 78274823934825, 0, 12635547508746, 0, 1585750445988, 0, 47322913536, 0, 991303875, 0, 10624700, 0, 82536, 0, 348, 0, 1]>],Snew);
    return Vf;
end function;