
// Make newform 795.2.m.a in Magma, downloaded from the LMFDB on 03 November 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_795_m();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_795_2_m_a();".
// 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_795_m();"
function MakeCharacter_795_m()
    N := 795;
    order := 4;
    char_gens := [266, 637, 691];
    v := [2, 3, 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_795_m_Hecke( : Kf := Kf)
    return MakeCharacter_795_m();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_795_2_m_a();".
// 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_795_2_m_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_795_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![2809, 0, 0, 0, 117600, 0, 0, 0, 50120, 0, 0, 0, 4400, 0, 0, 0, 120, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;