
// Make newform 1000.2.q.c in Magma, downloaded from the LMFDB on 21 June 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_1000_q();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1000_2_q_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_1000_q();"
function MakeCharacter_1000_q()
    N := 1000;
    order := 10;
    char_gens := [751, 501, 377];
    v := [10, 10, 7];
    // 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_1000_q_Hecke( : Kf := Kf)
    return MakeCharacter_1000_q();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1000_2_q_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_1000_2_q_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1000_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![6400, 102400, 1356800, -6211200, 7694560, 9415680, -33746940, 13365560, 52041221, -59530720, -23880517, 63079000, 13378921, -46785280, -16083805, 23012030, 13983715, -3809560, -3298662, 905720, 763409, -160150, -159697, 15730, 25770, -460, -2500, 0, 216, 0, -17, 0, 1]>],Snew);
    return Vf;
end function;