
// Make newform 6015.2.a.f in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6015_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6015_2_a_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_6015_a();"
function MakeCharacter_6015_a()
    N := 6015;
    order := 1;
    char_gens := [2006, 2407, 3211];
    v := [1, 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_6015_a_Hecke(Kf)
    return MakeCharacter_6015_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6015_2_a_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_6015_2_a_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6015_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-9576, -15988, 502508, -60033, -7352238, 2799603, 50578135, -16787305, -195527074, 40507591, 469075362, -35887202, -742710193, -29245863, 808925830, 111451939, -622946373, -138166234, 344827702, 102143347, -138104095, -50652158, 39849564, 17581368, -8125683, -4331882, 1115960, 754417, -90585, -90766, 2093, 7174, 344, -335, -34, 7, 1]>],Snew);
    return Vf;
end function;