
// Make newform 102.2.i.b in Magma, downloaded from the LMFDB on 01 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_102_i();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_102_2_i_b();".
// 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_102_i();"
function MakeCharacter_102_i()
    N := 102;
    order := 16;
    char_gens := [35, 37];
    v := [8, 5];
    // 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_102_i_Hecke( : Kf := Kf)
    return MakeCharacter_102_i();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_102_2_i_b();".
// 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_102_2_i_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_102_i();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![591872, 4108288, 12921856, 23968768, 28982656, 24078592, 14155328, 6000640, 1867652, 264640, -252624, -363456, -246824, -103776, 10144, 10432, 7624, 7296, 1256, 224, 156, -16, 8, 0, 1]>],Snew);
    return Vf;
end function;