
// Make newform 950.2.u.g in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_u();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_u_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_950_u();"
function MakeCharacter_950_u()
    N := 950;
    order := 18;
    char_gens := [77, 401];
    v := [9, 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_950_u_Hecke(Kf)
    return MakeCharacter_950_u();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_u_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_950_2_u_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_u();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![4096, 0, -5870592, 0, 2368468224, 0, 12804263936, 0, 32232813984, 0, 27301407156, 0, 23812992729, 0, 8461329102, 0, 1692376947, 0, 42298246, 0, -10874079, 0, -6862662, 0, 27324, 0, 27396, 0, 18738, 0, -2188, 0, 153, 0, -18, 0, 1]>,<7,R![342102016, 0, -625528209408, 0, 1142870069664768, 0, -1641943678554112, 0, 1456253412007680, 0, -803749160667648, 0, 322264218028032, 0, -93032116388160, 0, 20340429220272, 0, -3292991973584, 0, 410153448792, 0, -39068349072, 0, 2907053073, 0, -166535361, 0, 7420923, 0, -248692, 0, 6195, 0, -102, 0, 1]>],Snew);
    return Vf;
end function;