
// Make newform 6025.2.a.j in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6025_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6025_2_a_j();".
// 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_6025_a();"
function MakeCharacter_6025_a()
    N := 6025;
    order := 1;
    char_gens := [2652, 2176];
    v := [1, 1];
    // 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_6025_a_Hecke(Kf)
    return MakeCharacter_6025_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6025_2_a_j();".
// 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_6025_2_a_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-409, 3109, 37150, 57162, -191509, -464134, 270657, 1187034, 18465, -1523952, -413835, 1131457, 480786, -511289, -281530, 140217, 98096, -21526, -21093, 1209, 2741, 127, -197, -23, 6, 1]>,<3,R![-832, -56040, -275653, 35363, 2134197, 2207651, -4903242, -7935606, 3598698, 11043542, 1188881, -7370134, -3095890, 2355933, 1774706, -226746, -475866, -63895, 60865, 20189, -2331, -2010, -196, 59, 15, 1]>],Snew);
    return Vf;
end function;