
// Make newform 375.2.i.d in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_375_i();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_375_2_i_d();".
// 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_375_i();"
function MakeCharacter_375_i()
    N := 375;
    order := 10;
    char_gens := [251, 127];
    v := [10, 7];
    // 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_375_i_Hecke(Kf)
    return MakeCharacter_375_i();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_375_2_i_d();".
// 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_375_2_i_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_375_i();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, 0, 4, 0, 1932, 0, -58037, 0, 681588, 0, -147172, 0, 64293, 0, -19372, 0, 4268, 0, -717, 0, 132, 0, -16, 0, 1]>],Snew);
    return Vf;
end function;