
// Make newform 603.2.f.c in Magma, downloaded from the LMFDB on 25 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_603_f();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_603_2_f_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_603_f();"
function MakeCharacter_603_f()
    N := 603;
    order := 3;
    char_gens := [470, 136];
    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_603_f_Hecke(Kf)
    return MakeCharacter_603_f();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_603_2_f_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_603_2_f_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_603_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![7144929, 175848651, 8569435077, 48663539064, 3855626357055, 27569729233212, 932456939334616, 4762764059291841, 131201809216604312, 911161267503195977, 9039015818227259676, 40746814307703028637, 247375574230331558181, 825162171645925699912, 3992063113778939596832, 10765723364000705490730, 45309900996574735203895, 101714486283715637432437, 390125172157946082520794, 744449488803920372815908, 2669191586163604028509123, 4387692454421904592383608, 14914865032039723748652717, 21414590707442338629671357, 69400081733880589158794032, 88207470366179932241919803, 272781457036659814560564373, 311030132966144431947287992, 916294914547952610072493264, 948742953659226095138072002, 2656222018890250654326886675, 2524267814288844529112802755, 6702151841257934745631151646, 5897963716983435752098524760, 14830715819594429252371080207, 12172391174372422858989934504, 28975133489199915375124196294, 22303899794653669727655153647, 50280700707606066784681805685, 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100389007, -2287223, 4614996, -103446, 172297, -3528, 4930, -82, 97, -1, 1]>,<5,R![69500711094259764797645049, -910749388917642051434708304, 11063847127080622851979769268, -73624724606849357758330767906, 510599352394815269473635002028, -2441380747304024646211512904527, 13179900437041190436228319401879, -51510677256719701106451418293381, 233249831187647636676106695136707, -774314392880109599448154217354538, 3051742387914470953043824906245942, -8859450192177384651940781409285237, 30991392194976694931913782516727360, -79828720605224837668704678837950133, 250540878558884835370699958244167394, -579791039104470423761404414918312968, 1644202763984753107277511310677594657, -3446160302744462162858524654257007767, 8867634298249598150005268591330821122, -16958945356916777296188863821561380051, 39751269091035566756564396692170855675, -69773061063496822739806664526604420140, 149462776089126735266636907136158735630, -241974752907613293274750189257318249393, 475359185349151218416930139490118262471, 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-2148927955529641396, 1010996003732166973, -117440537013647689, 52261542866234943, -5802998104221424, 2435741744795664, -257209832783762, 101547563760689, -10124830074142, 3749029317705, -349422715348, 120965515695, -10392114552, 3351244309, -260039364, 77762775, -5284022, 1456634, -82342, 20749, -884, 201, -5, 1]>],Snew);
    return Vf;
end function;