
// Make newform 260.2.bg.c in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_260_bg();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_260_2_bg_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_260_bg();"
function MakeCharacter_260_bg()
    N := 260;
    order := 12;
    char_gens := [131, 157, 41];
    v := [6, 9, 10];
    // 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_260_bg_Hecke(Kf)
    return MakeCharacter_260_bg();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_260_2_bg_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_260_2_bg_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_260_bg();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![43096964632701710851178496, 0, 0, 0, -7902730308709362646821666816, 0, 0, 0, 1240184689693823082338713939968, 0, 0, 0, -35385964521257517729782714025984, 0, 0, 0, 740642714932888643713684290797824, 0, 0, 0, -5685348080440477475623852023080960, 0, 0, 0, 30221491395672331906138950362662912, 0, 0, 0, -90294141650787440006079957006642944, 0, 0, 0, 189610966201625033634197220295668352, 0, 0, 0, -219368144306860451623971437959223808, 0, 0, 0, 175213174404867233273402808388386144, 0, 0, 0, -100737300441391671072616216744036128, 0, 0, 0, 44268535769379925859740314351502960, 0, 0, 0, -15149967382814563829297815880416240, 0, 0, 0, 4134550706347385021223573900296936, 0, 0, 0, -907191667443920647920580789308192, 0, 0, 0, 162031089979483627719423878281241, 0, 0, 0, -23685097338747637678450969031422, 0, 0, 0, 2859335911296101792070943235503, 0, 0, 0, -286643430293751552383697758134, 0, 0, 0, 24022972703665976984568420311, 0, 0, 0, -1689767747691181029711472564, 0, 0, 0, 100185699945283227862273850, 0, 0, 0, -5016021757495165571281708, 0, 0, 0, 212384166066291425332149, 0, 0, 0, -7596302234620343068794, 0, 0, 0, 229109634498088950897, 0, 0, 0, -5800313077844589562, 0, 0, 0, 122660326634845709, 0, 0, 0, -2148591424851964, 0, 0, 0, 30930126607498, 0, 0, 0, -360758553092, 0, 0, 0, 3362718895, 0, 0, 0, -24290390, 0, 0, 0, 131231, 0, 0, 0, -478, 0, 0, 0, 1]>,<17,R![277124435060383572862529405003906250000, 225551053650402080474096711025000000000, 91787788023314523852212704080000000000, 39002039645050788447931242519375000000, -38198167230651441813684379223212500000, -38364822700375518859268507630535000000, -15828706542393340307506277467182000000, -7522884152151822674080945537669200000, 3978353155946749521273512441962290000, 5283303862867270394945199622594596000, 2397424541929295814881427767519203200, 1265043097265600556255129010914529440, 167870653324326657588405893577203304, -202003709290754895731935661034772224, -113588248398857214989560580109149568, -63513171798819236947623106693026864, -14649274786602426806134633113251712, 5173641708559915013571222793117872, 3625180898152476070263056783690016, 2112892665570980136034967068154064, 603853163030102791202649435604104, -72996493148290866974990733521208, -76550787016931998566623113263072, -45890382873926387079811940184936, -14033342434347953341112582624655, 572440459677325302999460558320, 1166033692635622758676230537312, 718864050133035767870909632728, 236064283462326815705362029306, 5581157943786310147784258424, -11848969276941350286041076000, -7948155195604835951049413628, -2793202813649030151828166043, -183405244011421568906116128, 82489347080058284732294976, 64483796077804425516882564, 24851256229107182743294918, 2635608569219556552890080, -279427543564348115251032, -354111495042736941004228, -154174325186289792625638, -20585070243418127074608, -10065374555313870976, 1386646833813475798992, 708832523122505816482, 112877764890580122216, 7090352622094736688, -3199448567155085180, -2211556878925592771, -396977993855988560, -35743935610912896, 4335486108852972, 5048102689774378, 1006669860225920, 110721504683896, 2175062145060, -7348544270550, -1652759838560, -196176806368, -13941817248, 7447475830, 1914607704, 244012400, 28630684, -3127227, -1233888, -161920, -21916, 474, 520, 72, 12, 1]>],Snew);
    return Vf;
end function;