
// Make newform 1175.2.c.h in Magma, downloaded from the LMFDB on 30 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1175_c();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1175_2_c_h();".
// 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_1175_c();"
function MakeCharacter_1175_c()
    N := 1175;
    order := 2;
    char_gens := [377, 851];
    v := [1, 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_1175_c_Hecke(Kf)
    return MakeCharacter_1175_c();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1175_2_c_h();".
// 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_1175_2_c_h( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1175_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![13689, 0, 186481, 0, 1006606, 0, 2848477, 0, 4692000, 0, 4761539, 0, 3116995, 0, 1359366, 0, 401903, 0, 80720, 0, 10833, 0, 929, 0, 46, 0, 1]>,<11,R![-162816, -747008, -251392, 1201920, 5248, -628608, 212064, 33720, -22396, 612, 781, -66, -9, 1]>],Snew);
    return Vf;
end function;