
// Make newform 1155.2.l.f in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1155_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1155_2_l_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_1155_l();"
function MakeCharacter_1155_l()
    N := 1155;
    order := 2;
    char_gens := [386, 232, 661, 211];
    v := [1, 2, 2, 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_1155_l_Hecke(Kf)
    return MakeCharacter_1155_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1155_2_l_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_1155_2_l_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1155_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-32, -400, -1340, 876, 10202, 5784, -25191, -19438, 29705, 21856, -20275, -12178, 8561, 3728, -2237, -634, 347, 56, -29, -2, 1]>,<17,R![-18091520, 8692864, 165682064, 93590816, -288310328, -269949872, 118520520, 189126632, 8033804, -50229300, -11041120, 5804480, 1897072, -328436, -146479, 9008, 5899, -96, -121, 0, 1]>],Snew);
    return Vf;
end function;