
// Make newform 930.2.v.a in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_v();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_v_a();".
// 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_v();"
function MakeCharacter_930_v()
    N := 930;
    order := 10;
    char_gens := [311, 187, 871];
    v := [5, 10, 3];
    // 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_v_Hecke(Kf)
    return MakeCharacter_930_v();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_v_a();".
// 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_v_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_v();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![156850849936, -368852411048, 2765986859508, -1568989049770, 9433852395739, -2167866093995, 15362812677942, -1442654125544, 11478997344381, -646762248628, 8422585889893, 65440814015, 5361710909130, 217726535038, 2531564155165, 106573350102, 695080721255, 13973369557, 186906545071, 5233320857, 44687170055, -128611888, 9159299254, 283272497, 973138735, -29928021, 269482124, 1562023, 15747815, -57830, 2986055, -168946, 233524, -1468, 15571, -1751, 971, -159, 51, -6, 1]>],Snew);
    return Vf;
end function;