
// Make newform 930.2.bg.g in Magma, downloaded from the LMFDB on 17 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_g();".
// 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_g();".
// 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_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_bg();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![5382400, -7888000, -31769600, 7008000, 213939600, 258377200, -34331000, -25498350, 116758355, 1354635, 4936835, 143160, -3950800, -255930, 391610, -146085, 82621, -6559, -4220, 2484, -421, 4, 30, -9, 1]>],Snew);
    return Vf;
end function;