
// Make newform 275.2.z.c in Magma, downloaded from the LMFDB on 28 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_275_z();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_275_2_z_c();".
// 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_275_z();"
function MakeCharacter_275_z()
    N := 275;
    order := 10;
    char_gens := [177, 101];
    v := [5, 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_275_z_Hecke(Kf)
    return MakeCharacter_275_z();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_275_2_z_c();".
// 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_275_2_z_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_275_z();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, 0, -71, 0, 2132, 0, -10603, 0, 1423681, 0, -2806839, 0, 2642317, 0, -1330529, 0, 961802, 0, -411465, 0, 113853, 0, -20142, 0, 5502, 0, -694, 0, 89, 0, -10, 0, 1]>],Snew);
    return Vf;
end function;