
// Make newform 735.2.y.g in Magma, downloaded from the LMFDB on 22 January 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_735_y();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_735_2_y_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_735_y();"
function MakeCharacter_735_y()
    N := 735;
    order := 12;
    char_gens := [491, 442, 346];
    v := [6, 9, 4];
    // 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_735_y_Hecke( : Kf := Kf)
    return MakeCharacter_735_y();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_735_2_y_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_735_2_y_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_735_y();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![256, 0, 0, 0, -18560, 0, 0, 0, 1090864, 0, 0, 0, -18088840, 0, 0, 0, 239693409, 0, 0, 0, -184875636, 0, 0, 0, 113473930, 0, 0, 0, -17766888, 0, 0, 0, 1979523, 0, 0, 0, -105632, 0, 0, 0, 4074, 0, 0, 0, -76, 0, 0, 0, 1]>,<11,R![22663495936, 0, -26582457344, 0, 19823248768, 0, -8904326400, 0, 2890968368, 0, -623527840, 0, 99309496, 0, -11249960, 0, 955849, 0, -57038, 0, 2451, 0, -62, 0, 1]>,<13,R![33856, -129536, 247808, 321280, 186352, 41056, 3328, -160, 625, 124, 8, -4, 1]>,<17,R![65536, 0, 0, 0, -62717952, 0, 0, 0, 46676615168, 0, 0, 0, -12757129560064, 0, 0, 0, 2710733921813248, 0, 0, 0, -1376615836959232, 0, 0, 0, 676518026435232, 0, 0, 0, -10572970183536, 0, 0, 0, 131887163297, 0, 0, 0, -440592322, 0, 0, 0, 1078419, 0, 0, 0, -1218, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;