
// Make newform 6025.2.a.l in Magma, downloaded from the LMFDB on 24 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_l();".
// 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_l();".
// 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_l( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![41303, 112017, -1157743, -2518861, 13406855, 24771707, -85017638, -142699144, 331026946, 538390433, -836972727, -1403012129, 1406075875, 2596782129, -1555220380, -3468989004, 1049378864, 3378345232, -272873630, -2411764697, -220810932, 1262094492, 296654484, -479933736, -177279357, 129349556, 67510849, -23176483, -17592761, 2221315, 3167203, 50678, -383558, -47342, 28938, 6489, -1090, -418, 0, 11, 1]>,<3,R![-4723, 79434, 1921618, -3394188, -92514659, 82707660, 1137364042, -630442248, -6389115625, 2205403295, 20360585773, -3856604066, -41028323095, 2598137275, 55634179445, 2295652757, -52748619752, -6771501482, 35855044773, 7227472980, -17764640875, -4705779761, 6476874027, 2090921732, -1741109729, -662854624, 342388092, 152778596, -48109412, -25690505, 4566377, 3120101, -249314, -266509, 1998, 15185, 724, -518, -47, 8, 1]>],Snew);
    return Vf;
end function;