
// Make newform 950.2.h.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_h();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_h_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_950_h();"
function MakeCharacter_950_h()
    N := 950;
    order := 5;
    char_gens := [77, 401];
    v := [1, 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_950_h_Hecke(Kf)
    return MakeCharacter_950_h();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_h_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_950_2_h_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_h();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![16, 488, 10600, 136304, 1180753, 6502208, 25795202, 45070293, 65385789, 54787976, 125140426, -27936489, 330548960, -312367000, 597794105, -389525253, 472199760, -288920571, 305397031, -204155314, 184614662, -122226138, 91577827, -48188674, 26568184, -11692305, 6470113, -3093969, 1605041, -628317, 271335, -95871, 37078, -11690, 4448, -1360, 465, -113, 29, -5, 1]>],Snew);
    return Vf;
end function;