
// Make newform 750.2.m.d in Magma, downloaded from the LMFDB on 09 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_750_m();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_750_2_m_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_750_m();"
function MakeCharacter_750_m()
    N := 750;
    order := 25;
    char_gens := [251, 127];
    v := [25, 12];
    // 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_750_m_Hecke( : Kf := Kf)
    return MakeCharacter_750_m();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_750_2_m_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_750_2_m_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_750_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![136796229623581759376507498490810597376, -5236922437562393734348171125522644336640, 90145460176646833414694978251518048993280, -586624942608145576167432486826571264163840, 5177195488634549481663665817177440687226880, -11092401853272246278591934339484554234462208, 105870678541594348757089180399928751594618880, -35811777207443600681449851875217461832540160, 1612228016585685882356643793381038276087214080, -408254271001517993149843467772557746453135360, 14488994081716486449852134899419672601616421888, -9227217627604718549711764720693418138800944640, 161901244537640850756887612920186467266732180480, 68299246835920664655899381119610300103494476160, 1128061793185830720580298383080238072514388711680, 410616944676122143507341507432693620102650677504, 3733348335700238661882795537099758020501729148400, 4209856978581801831404274650507656602988796725400, 15331108209824887646407010369884047411852948751800, 20782042346428557607091627438147422045389038662900, 51635409128287766273745343112805582826359508380605, 72926555583680732808253046876712697194393113768075, 134470988942231661730030145023413356808534265502825, 175429770471579901003199378139981854528672849232025, 289523486602585319070799392607988905498608789313125, 400087853485343606555491160035082744498749152398100, 613154859219053653635017848398129615356277460396200, 778741796370252797915087804479166071743417890785475, 1016231367597970638398237335147015318391603220975700, 1182038478127011483407477097960021605703179016420450, 1441872241918344440133166722331500054549753790720170, 1630678417774441131399718756567013934724091904278400, 1875974168775584222136300840645770824715306471721600, 1995818479957107511115130631475536665258779452832325, 2120869492613436810581611346534093987450581134799125, 2118115138316388337178225173099227203100953149506740, 2116452259163203913562423886951228912211298697590675, 2014375846679185769222670073767446545141928224054450, 1909842846497126402093415546224273185506461783840400, 1728831393291150129187981186047537686584908958593775, 1546342406170433645697398789914355203670737815648360, 1321813527746957722454948367964681831049850923566650, 1113034530864373967688793107578709787182426248877400, 899831303193394253190795843209940907699216603837675, 717124228938323023579665293383606978358760191501400, 550755436014676045566811105786326654072713893900580, 416565177346584972142189391760486869273745563991075, 303833630182214879479271094047235706567144766076450, 217830276342222273060654541397158490472866594224275, 150659437466178757307211608312985243134277890743000, 102375200736226567341950114848259829310350210802090, 67194134832111522826163417350655997110862213897475, 43354712520552005556440624364904936931491059503675, 27044341054944272868731808393438555459772680527975, 16586507750238899129572030336092903465681565795525, 9831824912480945760167516371386129979466666478650, 5728235059322118286329490210387377416411465546600, 3222866794558185042793549950261630602597319387950, 1782880220187244652524478872995098334957346541650, 951966902873909137849340006391223031956707086975, 500590306170897723643141085849049193669321556035, 254029527366956228539939878375342307203053137075, 127292454547380233719528904203852074211181257650, 61522754314197425669425426356886524233131556050, 29459073489933129650802540339702313748255845475, 13586219723133848101472565764235534808567781770, 6232358802552054930934165817513854596900140900, 2746541424054322060822034550902496858689665400, 1210021898978367821418993505802365575490798050, 510111651007334621659146606544873824433240275, 216429185586712176947778761915798545896872130, 87358213577465131116785032430728433545843325, 35803854558475515865450951401951563309784950, 13842346524651636189963556988543951129753775, 5498905415668968329627700519885134409454750, 2035669943908642180492545503201893919066995, 786784281027196079642831863553823959431150, 278542501702326523717241793034850839162075, 105206585618142654861046103661253725406525, 35533198049025289543127167389399694896925, 13186222718012085807409250273769666591360, 4232259112203113868081131068834230735375, 1553395946558455495337728330249028670650, 471049998746594275827782264493761755925, 172438320229440512469583277049371588550, 48997581777306868301585572423272305075, 18080452531748982434210201836235559875, 4760121145023014127776249025101161175, 1794653127492810910804515750670415350, 431250164028945696485899202230165375, 168977465556833696539445064970656365, 36336654835134852424243706928471525, 15117771880230728576496319234744775, 2835575178393774009485775173664925, 1286713616331515237166290620832400, 203629050253331799630249042234705, 104246915684752323660569487939700, 13323020999086312041904052564450, 8037905884450494762763044079025, 781021232038414331673754718375, 589180972396690097337984583585, 39735958766177064341576762425, 40979337835748184175337509650, 1625285512622447013245128800, 2698162512456122212932081500, 39386880009573726364530440, 167760131953999697942572075, -1229132023606957675206375, 9826677302559479406635375, -255546196415574684770225, 541070101171729326679095, -22473491698439584967350, 27943381888758818378250, -1512619372744954897500, 1350617370460508871200, -86554521403233201500, 60958624162455000650, -4371532812909075475, 2562638532582166300, -198073974283846350, 100030170352830730, -8106315103339050, 3611241317399450, -300231950882850, 119987501864500, -10049464870021, 3645801818140, -302388454155, 100398374840, -8093296280, 2473954088, -189704455, 53591335, -3807480, 993435, -62583, 14990, -755, 165, -5, 1]>],Snew);
    return Vf;
end function;