
// Make newform 900.2.r.g in Magma, downloaded from the LMFDB on 18 March 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_900_r();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_900_2_r_g();".
// 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_r();"
function MakeCharacter_900_r()
    N := 900;
    order := 6;
    char_gens := [451, 101, 577];
    v := [3, 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_r_Hecke( : Kf := Kf)
    return MakeCharacter_900_r();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_900_2_r_g();".
// 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_2_r_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_900_r();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![7290000, 0, -17884800, 0, 27788076, 0, -26555616, 0, 18514873, 0, -8702080, 0, 2963314, 0, -620404, 0, 94189, 0, -9700, 0, 730, 0, -34, 0, 1]>,<13,R![12990084638976, 0, 8608675292928, 0, 3671056489536, 0, 904387851072, 0, 159246799344, 0, 18811362384, 0, 1651842648, 0, 106765272, 0, 5286408, 0, 193314, 0, 5247, 0, 93, 0, 1]>],Snew);
    return Vf;
end function;