
// Make newform 930.2.bg.i in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_bg();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bg_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_930_bg();"
function MakeCharacter_930_bg()
    N := 930;
    order := 15;
    char_gens := [311, 187, 871];
    v := [15, 15, 8];
    // 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_930_bg_Hecke(Kf)
    return MakeCharacter_930_bg();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bg_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_930_2_bg_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_bg();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![236421376, 507161984, 68515456, 1113476352, 5015510416, 1794606000, 8097056240, 6032725302, -302727709, 359651649, 1112298783, 281064422, -24831268, -11623534, -4876824, -1339203, 276927, 139225, 15822, -2690, -1127, -174, 8, 7, 1]>],Snew);
    return Vf;
end function;