
// Make newform 930.2.o.d in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_o();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_o_d();".
// 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_o();"
function MakeCharacter_930_o()
    N := 930;
    order := 6;
    char_gens := [311, 187, 871];
    v := [3, 6, 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_930_o_Hecke(Kf)
    return MakeCharacter_930_o();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_o_d();".
// 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_o_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_o();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![7744, -76472, 606441, -1512962, 3216592, -2403232, 2468701, 784232, 2353126, 619666, 379512, 61730, 32649, 4564, 1754, 156, 55, 4, 1]>,<11,R![3170478249, 0, 169253154993, 0, 7595312463844, 0, 69950311958447, 0, 467935199111521, 0, 1439895591632052, 0, 3206241461956713, 0, 1206850078476575, 0, 292533507702387, 0, 44390546841192, 0, 4895875513750, 0, 373848506414, 0, 21411510523, 0, 905877661, 0, 29350491, 0, 701046, 0, 12407, 0, 143, 0, 1]>],Snew);
    return Vf;
end function;