
// Make newform 930.2.k.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_k();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_k_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_930_k();"
function MakeCharacter_930_k()
    N := 930;
    order := 4;
    char_gens := [311, 187, 871];
    v := [4, 1, 2];
    // 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_k_Hecke(Kf)
    return MakeCharacter_930_k();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_k_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_930_2_k_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_k();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<13,R![6879707136, -45864714240, 152882380800, -265442033664, 284265676800, -269881638912, 603015118848, -1005292683264, 985913774080, -440063866880, 189403609088, -234902048256, 281320651840, -110027179648, 14573569152, -721621696, 16753494704, -4873120128, 358940224, 515396608, 371281836, -12574280, 1592264, 2751076, 1819129, 38260, 1352, 2428, 2474, 52, 0, 0, 1]>],Snew);
    return Vf;
end function;