Properties

Label 3.44.a
Level 3
Weight 44
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 2
Sturm bound 14
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 44 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_0(3))\).

Total New Old
Modular forms 15 7 8
Cusp forms 13 7 6
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(3\)Dim.
\(+\)\(4\)
\(-\)\(3\)

Trace form

\(7q \) \(\mathstrut +\mathstrut 6517038q^{2} \) \(\mathstrut -\mathstrut 10460353203q^{3} \) \(\mathstrut +\mathstrut 27552692534980q^{4} \) \(\mathstrut +\mathstrut 1142897486431650q^{5} \) \(\mathstrut +\mathstrut 33441853793523030q^{6} \) \(\mathstrut -\mathstrut 1518687877922879560q^{7} \) \(\mathstrut +\mathstrut 89162849355444024504q^{8} \) \(\mathstrut +\mathstrut 765932923920586514463q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 6517038q^{2} \) \(\mathstrut -\mathstrut 10460353203q^{3} \) \(\mathstrut +\mathstrut 27552692534980q^{4} \) \(\mathstrut +\mathstrut 1142897486431650q^{5} \) \(\mathstrut +\mathstrut 33441853793523030q^{6} \) \(\mathstrut -\mathstrut 1518687877922879560q^{7} \) \(\mathstrut +\mathstrut 89162849355444024504q^{8} \) \(\mathstrut +\mathstrut 765932923920586514463q^{9} \) \(\mathstrut +\mathstrut 3072194289085163902740q^{10} \) \(\mathstrut -\mathstrut 19035765706499831738724q^{11} \) \(\mathstrut -\mathstrut 325471887738193227553548q^{12} \) \(\mathstrut -\mathstrut 2617160217501477947686246q^{13} \) \(\mathstrut -\mathstrut 22940835489552033441320736q^{14} \) \(\mathstrut -\mathstrut 22577669540410756207434570q^{15} \) \(\mathstrut +\mathstrut 288968962871170267541644816q^{16} \) \(\mathstrut +\mathstrut 132894232119725057809930494q^{17} \) \(\mathstrut +\mathstrut 713087710091653042434702942q^{18} \) \(\mathstrut -\mathstrut 5821548062418507223994361052q^{19} \) \(\mathstrut -\mathstrut 11361818898070054340117998440q^{20} \) \(\mathstrut -\mathstrut 18281043905959596222646348248q^{21} \) \(\mathstrut -\mathstrut 98391603692820471055636363992q^{22} \) \(\mathstrut -\mathstrut 50939297339004823737048394440q^{23} \) \(\mathstrut -\mathstrut 698441214009721194959001259176q^{24} \) \(\mathstrut +\mathstrut 3988249344494775779307363017425q^{25} \) \(\mathstrut +\mathstrut 7876043696489369220439735673364q^{26} \) \(\mathstrut -\mathstrut 1144561273430837494885949696427q^{27} \) \(\mathstrut -\mathstrut 50172114989349391656965649419200q^{28} \) \(\mathstrut +\mathstrut 21862341772501438182015618112506q^{29} \) \(\mathstrut -\mathstrut 79978769266496152864435752377340q^{30} \) \(\mathstrut +\mathstrut 96284802644006465760845197742288q^{31} \) \(\mathstrut +\mathstrut 1085000407788608986452656443411680q^{32} \) \(\mathstrut -\mathstrut 381448984862347506928657111335948q^{33} \) \(\mathstrut -\mathstrut 1717914447357080006255834378640420q^{34} \) \(\mathstrut -\mathstrut 2846930853668343686195953055547120q^{35} \) \(\mathstrut +\mathstrut 3014787765028878333055422557630820q^{36} \) \(\mathstrut +\mathstrut 11827942294905789469146681908011250q^{37} \) \(\mathstrut +\mathstrut 18949776129019716968988077720644248q^{38} \) \(\mathstrut +\mathstrut 6564786091327381994846895875601438q^{39} \) \(\mathstrut +\mathstrut 120952775831830557694116594743526480q^{40} \) \(\mathstrut -\mathstrut 159660757593698934702193525404638922q^{41} \) \(\mathstrut +\mathstrut 41782017368824130786695041362790240q^{42} \) \(\mathstrut -\mathstrut 445385053821651313603552457774294788q^{43} \) \(\mathstrut +\mathstrut 514771999191844202349244122049730352q^{44} \) \(\mathstrut +\mathstrut 125054687646297505376512358426564850q^{45} \) \(\mathstrut +\mathstrut 1919913529753176286697775003240723888q^{46} \) \(\mathstrut +\mathstrut 1007386372706766980950842143847661776q^{47} \) \(\mathstrut -\mathstrut 2528200230117957060664761051515338032q^{48} \) \(\mathstrut -\mathstrut 3134434768153824860259922682917637217q^{49} \) \(\mathstrut -\mathstrut 215835506759972611665719817470649150q^{50} \) \(\mathstrut -\mathstrut 4748262629032092633291700441781677974q^{51} \) \(\mathstrut +\mathstrut 5928474039780845142980093577783102104q^{52} \) \(\mathstrut -\mathstrut 37123865678022673989384726402380809230q^{53} \) \(\mathstrut +\mathstrut 3659173836771121779525330038974083270q^{54} \) \(\mathstrut +\mathstrut 25137017157329762212611755271169823880q^{55} \) \(\mathstrut -\mathstrut 52731379615541759245045493678855898240q^{56} \) \(\mathstrut -\mathstrut 6618467412659334504124654801940360628q^{57} \) \(\mathstrut +\mathstrut 331896989149921437949417385049369480036q^{58} \) \(\mathstrut -\mathstrut 209295975577175279210608813015855660308q^{59} \) \(\mathstrut -\mathstrut 297902712533327459906118070732244448840q^{60} \) \(\mathstrut -\mathstrut 370211751147778043692096224549283789078q^{61} \) \(\mathstrut +\mathstrut 762371962973790329183593532367846459120q^{62} \) \(\mathstrut -\mathstrut 166173292408603127151712517494363868040q^{63} \) \(\mathstrut +\mathstrut 2808223714597123329186355443560276247616q^{64} \) \(\mathstrut +\mathstrut 625625274103466076579712839407412892140q^{65} \) \(\mathstrut -\mathstrut 2578994607297142277040339530297057413368q^{66} \) \(\mathstrut +\mathstrut 2322037304336064260539793412484562855924q^{67} \) \(\mathstrut -\mathstrut 8446047834679208486952132913331032294776q^{68} \) \(\mathstrut +\mathstrut 2934127570990444387065783796502603683944q^{69} \) \(\mathstrut -\mathstrut 12130582077585371798236302781268995312320q^{70} \) \(\mathstrut +\mathstrut 15241554579473183067868746037765841779944q^{71} \) \(\mathstrut +\mathstrut 9756108844558003479850015126262646057336q^{72} \) \(\mathstrut +\mathstrut 36750445086504587297962708685796828639350q^{73} \) \(\mathstrut -\mathstrut 26735922391585513239864278098991204112156q^{74} \) \(\mathstrut -\mathstrut 3529415151601739577719021862742682341125q^{75} \) \(\mathstrut -\mathstrut 130858737506455417609661427645819982824112q^{76} \) \(\mathstrut -\mathstrut 54723580632550426020219452913802424424480q^{77} \) \(\mathstrut -\mathstrut 45251165210554144177882275276918866663676q^{78} \) \(\mathstrut -\mathstrut 62285506214556153263852659257744365976640q^{79} \) \(\mathstrut +\mathstrut 473370600052077409250985876263720552715360q^{80} \) \(\mathstrut +\mathstrut 83807606277934138520219180187019329739767q^{81} \) \(\mathstrut -\mathstrut 60325172294638954945820531986037624103540q^{82} \) \(\mathstrut +\mathstrut 297775298846470618033245296257764909541476q^{83} \) \(\mathstrut +\mathstrut 347336094199013425123163701821074057852736q^{84} \) \(\mathstrut -\mathstrut 388659198907389679147824610988098149552540q^{85} \) \(\mathstrut -\mathstrut 593945295228698781571501136249070550466904q^{86} \) \(\mathstrut -\mathstrut 819521803998802443677617111025903237246466q^{87} \) \(\mathstrut +\mathstrut 651649734797744001253688844880958828678304q^{88} \) \(\mathstrut -\mathstrut 376887070672087582858715444216705586586362q^{89} \) \(\mathstrut +\mathstrut 336156393527303888043111593029783219332660q^{90} \) \(\mathstrut +\mathstrut 1120334119952645800083619159231904049934288q^{91} \) \(\mathstrut +\mathstrut 3252061132085359551594317108350167852059040q^{92} \) \(\mathstrut -\mathstrut 2198554284804227085242625094453339705081680q^{93} \) \(\mathstrut -\mathstrut 4869124258648927645343432668946339360463552q^{94} \) \(\mathstrut +\mathstrut 8450283823986855920702119042300320211171320q^{95} \) \(\mathstrut -\mathstrut 17424290501374393618143926382189653236318368q^{96} \) \(\mathstrut +\mathstrut 1062362705477408245549478273344689659661614q^{97} \) \(\mathstrut +\mathstrut 4229065919565839963906007000405390204075486q^{98} \) \(\mathstrut -\mathstrut 2082874240949520774932861767757129723309316q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.44.a.a \(3\) \(35.133\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(4857024\) \(31381059609\) \(-5\!\cdots\!70\) \(-1\!\cdots\!88\) \(-\) \(q+(1619008-\beta _{1})q^{2}+3^{21}q^{3}+(-593686009856+\cdots)q^{4}+\cdots\)
3.44.a.b \(4\) \(35.133\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(1660014\) \(-41841412812\) \(16\!\cdots\!20\) \(11\!\cdots\!28\) \(+\) \(q+(415003+\beta _{1})q^{2}-3^{21}q^{3}+(7333437011374+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{44}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)