
// Make newform 950.2.h.e in Magma, downloaded from the LMFDB on 19 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_e();".
// 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_e();".
// 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_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_h();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![54405376, 13158784, 248248320, 395127136, 1075411344, -465457656, 4400354048, -194625310, 6201865369, -1846017928, 27322786692, -22216902921, 45345045943, -27625872844, 49427815352, -18502230815, 40156731242, -10268427944, 26128857503, -6569546837, 13287486048, -3339871107, 5356512057, -1107952946, 1678074074, -248064178, 429080589, -46934928, 93563368, -8514725, 17608139, -1066215, 2690387, -19105, 350977, 7321, 41174, 1454, 4018, 242, 323, 31, 21, 1, 1]>],Snew);
    return Vf;
end function;