
// Make newform 6013.2.a.f in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6013_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6013_2_a_f();".
// 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_6013_a();"
function MakeCharacter_6013_a()
    N := 6013;
    order := 1;
    char_gens := [5155, 3438];
    v := [1, 1];
    // 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_6013_a_Hecke(Kf)
    return MakeCharacter_6013_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6013_2_a_f();".
// 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_6013_2_a_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6013_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![82552988, -27295135220, -206512941142, 5340098049566, 23086025991908, -413583783992625, -1182622354376310, 17882739545089967, 36433437613647574, -498149910231434808, -754231013178234428, 9676207905032249349, 11121695216768354188, -137902989121432555243, -120801087697526350395, 1495060322632549254259, 984314703802528310411, -12672173987013599080974, -6042349383539526723807, 85809790149454381923127, 27454364979570262288284, -472402393774522389297841, -85493250656968961985738, 2144979593912058735773944, 119398726847848552237384, -8129488284942559390085253, 478627233260659779918244, 25976751755846776291191250, -4281641948482327227889101, -70575915551101577563561232, 18634986480157852632348820, 164201608559103411136486128, -58829089537386480320119233, -329123939954889275800647374, 147881679815967311341863437, 571191730585105859705669596, -307960870751341943883298308, -861827155046219211904708784, 543029700217734116781001573, 1134093101831444537245062884, -822214370014564321903668509, -1304402992995394097143139346, 1079617725141154383498787193, 1312649035604135172386984539, -1238478443553213699387130171, -1155161090352778999242965196, 1248338766199604253790807884, 886598388356015692216231362, -1110646054494721656103632897, -589774996160807619717329129, 875366699819488149181465958, 335671409682091768617291984, -612936850981348371440622398, -158998617865120271329071739, 382122512284661774936060583, 58437234198773894456084355, -212437482057498870925862135, -12654868401181890785612631, 105418535173207541097799401, -2551348650574971531319283, -46708866575674169420574738, 4734376487167152295961783, 18471817789996781299488099, -3225490415642214648436859, -6511972060979982178137755, 1606754484331695609964880, 2041748824623901178598295, -655250915673649860348931, -567179489572414115007732, 227691128888534421473142, 138745623524343678615266, -68653892700017870275463, -29593075465277843724715, 18126265085136183468271, 5409542188360349869205, -4208896034275037355320, -819393905904458316516, 860723822144339196702, 94671876265486792322, -154906865463429920779, -5905644644979110835, 24469664290936616721, -619396975438813956, -3376718564314542617, 283087632925571565, 404155121805661510, -56910908822537469, -41508358605294499, 8315617107179137, 3598552795118481, -967279609766300, -256269806016181, 92035585216992, 14222286745602, -7199870154578, -535572840948, 459805612606, 5337513406, -23550392402, 972152849, 937320655, -84406982, -27405379, 3894756, 523528, -113449, -4409, 1981, -41, -16, 1]>],Snew);
    return Vf;
end function;