
// Make newform 6015.2.a.i in Magma, downloaded from the LMFDB on 25 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_i();".
// 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_i();".
// 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_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6015_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-11944, -101036, 1500576, 13750921, -21452362, -347260284, -77680615, 3369366605, 2820225731, -15223350944, -16013270273, 39960414598, 45180964381, -69072441589, -78912245966, 84671160417, 94151141990, -77123623067, -81096332801, 53807600690, 52177099118, -29326785175, -25625271053, 12639283675, 9734768205, -4334617598, -2880095879, 1184504633, 664364021, -257068680, -118940032, 43944398, 16340930, -5832956, -1688384, 587681, 126812, -43354, -6530, 2205, 206, -69, -3, 1]>],Snew);
    return Vf;
end function;