Properties

Label 2.66.a
Level 2
Weight 66
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 66 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{66}(\Gamma_0(2))\).

Total New Old
Modular forms 17 5 12
Cusp forms 15 5 10
Eisenstein series 2 0 2

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

\(2\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 4294967296q^{2} \) \(\mathstrut +\mathstrut 4133618558416404q^{3} \) \(\mathstrut +\mathstrut 92233720368547758080q^{4} \) \(\mathstrut -\mathstrut 70844492277858340250850q^{5} \) \(\mathstrut +\mathstrut 7883406622088398551121920q^{6} \) \(\mathstrut +\mathstrut 7001440406811157707981723688q^{7} \) \(\mathstrut +\mathstrut 79228162514264337593543950336q^{8} \) \(\mathstrut +\mathstrut 4280010205873910625488759430465q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 4294967296q^{2} \) \(\mathstrut +\mathstrut 4133618558416404q^{3} \) \(\mathstrut +\mathstrut 92233720368547758080q^{4} \) \(\mathstrut -\mathstrut 70844492277858340250850q^{5} \) \(\mathstrut +\mathstrut 7883406622088398551121920q^{6} \) \(\mathstrut +\mathstrut 7001440406811157707981723688q^{7} \) \(\mathstrut +\mathstrut 79228162514264337593543950336q^{8} \) \(\mathstrut +\mathstrut 4280010205873910625488759430465q^{9} \) \(\mathstrut +\mathstrut 337930938987470828035602854707200q^{10} \) \(\mathstrut +\mathstrut 7618362444343764013557498728179260q^{11} \) \(\mathstrut +\mathstrut 76251803645443620481025441859108864q^{12} \) \(\mathstrut +\mathstrut 882232885765420334201808050793817414q^{13} \) \(\mathstrut +\mathstrut 6803913574135557746113036325790679040q^{14} \) \(\mathstrut -\mathstrut 165869399198448371842533041273942200200q^{15} \) \(\mathstrut +\mathstrut 1701411834604692317316873037158841057280q^{16} \) \(\mathstrut -\mathstrut 699431199975967287511256391699769193382q^{17} \) \(\mathstrut +\mathstrut 54688046875378802693745458742371033284608q^{18} \) \(\mathstrut -\mathstrut 215797600433727494753707613754433376524700q^{19} \) \(\mathstrut -\mathstrut 1306850218081545431136438477056118462873600q^{20} \) \(\mathstrut +\mathstrut 30443141210675727163896322101419389667840160q^{21} \) \(\mathstrut -\mathstrut 34407601299804566546070673016669303878975488q^{22} \) \(\mathstrut -\mathstrut 104566143245074550889373169195452729735243656q^{23} \) \(\mathstrut +\mathstrut 145423184386651800763257989747180776949022720q^{24} \) \(\mathstrut +\mathstrut 5222815973812689992833539864389023280667966875q^{25} \) \(\mathstrut +\mathstrut 1315764479050205968931892579612946188908625920q^{26} \) \(\mathstrut +\mathstrut 108154104528163539963028302441214172940259640520q^{27} \) \(\mathstrut +\mathstrut 129153779331774315634960680592466989365285879808q^{28} \) \(\mathstrut +\mathstrut 1171901356388482342344411971093074800906153580950q^{29} \) \(\mathstrut +\mathstrut 2636047695217789092070144412157500828736395673600q^{30} \) \(\mathstrut +\mathstrut 6330506755320242122975820336302432496801315635360q^{31} \) \(\mathstrut +\mathstrut 1461501637330902918203684832716283019655932542976q^{32} \) \(\mathstrut +\mathstrut 39879294444584220584040633282302322814198186549488q^{33} \) \(\mathstrut -\mathstrut 36021307174538746358640453802001276944144882728960q^{34} \) \(\mathstrut -\mathstrut 372218224586284300861056362847849176534279130224400q^{35} \) \(\mathstrut +\mathstrut 78952252900620958774140821728608214427666680381440q^{36} \) \(\mathstrut -\mathstrut 3796574591615529074089308713364716756356228339444802q^{37} \) \(\mathstrut +\mathstrut 267335410113780242328820161186798526325139848560640q^{38} \) \(\mathstrut -\mathstrut 5192750444320907817264786716986040411323790842623720q^{39} \) \(\mathstrut +\mathstrut 6233725546090231562181116522837441861517306966835200q^{40} \) \(\mathstrut +\mathstrut 35772385403070962335047731365996323671787664820390610q^{41} \) \(\mathstrut +\mathstrut 94867057371610595257263342953447427034225718373384192q^{42} \) \(\mathstrut +\mathstrut 350346941095941448933482524047995791803323727120787164q^{43} \) \(\mathstrut +\mathstrut 140533982271569742575260309124088171618023518670684160q^{44} \) \(\mathstrut -\mathstrut 457212883913540336931885029604185305367305418651677050q^{45} \) \(\mathstrut -\mathstrut 1669042359869728607100831802554318733465623847847854080q^{46} \) \(\mathstrut -\mathstrut 4646380911000170258795696401836769347105474956211412752q^{47} \) \(\mathstrut +\mathstrut 1406597507006251490063556690525924837662007810771124224q^{48} \) \(\mathstrut -\mathstrut 1492129351102935371466979010126725467565631037366182115q^{49} \) \(\mathstrut -\mathstrut 20769275918226828691437122316804487156160327057408000000q^{50} \) \(\mathstrut +\mathstrut 74851968734293288352325441533429824399212255083256806760q^{51} \) \(\mathstrut +\mathstrut 16274324257124943388074079241916687299311250450912641024q^{52} \) \(\mathstrut +\mathstrut 335677682346300958056164096291669515440665473899464980494q^{53} \) \(\mathstrut +\mathstrut 431935331265433676799136624090133427160061237003078860800q^{54} \) \(\mathstrut -\mathstrut 122303479920127600487377641644361911833275741992778946200q^{55} \) \(\mathstrut +\mathstrut 125510052401717073823312112432628728263396808710569328640q^{56} \) \(\mathstrut -\mathstrut 1435524027006552343277813430410848729092758221985585213040q^{57} \) \(\mathstrut -\mathstrut 463713973433259568312809449560182624145045665678549319680q^{58} \) \(\mathstrut +\mathstrut 3394625272218993571894661733741175653526062991894700889900q^{59} \) \(\mathstrut -\mathstrut 3059750356673741354328954615360195867853249801442505523200q^{60} \) \(\mathstrut +\mathstrut 1520772410473144755394714234498724572536428901978405638710q^{61} \) \(\mathstrut +\mathstrut 24605740180163429068226621132519593106424989224621291077632q^{62} \) \(\mathstrut +\mathstrut 135802714150119560665896310122169518736801764333945454076424q^{63} \) \(\mathstrut +\mathstrut 31385508676933403819178947116038332080511777222320172564480q^{64} \) \(\mathstrut +\mathstrut 64895485235702121487226607312575215983367937836195523451300q^{65} \) \(\mathstrut -\mathstrut 149809626692567909855591124779109907632091308722545345167360q^{66} \) \(\mathstrut -\mathstrut 147204622169015019103541524984654002213146800760232231332012q^{67} \) \(\mathstrut -\mathstrut 12902228343124234841563922514387832354408299542877214605312q^{68} \) \(\mathstrut -\mathstrut 2338952611656294569618620625821052274589789954278426765004320q^{69} \) \(\mathstrut -\mathstrut 231922377657414178457725845294759625323592133174100806860800q^{70} \) \(\mathstrut +\mathstrut 383895739208569607456368041152734954962343140940927969843560q^{71} \) \(\mathstrut +\mathstrut 1008816404601144090256994255289991135553039040467067394326528q^{72} \) \(\mathstrut +\mathstrut 1439430039400866536657771416898150420909402155311949577010034q^{73} \) \(\mathstrut +\mathstrut 2387610310641129678148832608798612527454897477792791202365440q^{74} \) \(\mathstrut +\mathstrut 9190450143105793808196455447938438580377589686680570076987500q^{75} \) \(\mathstrut -\mathstrut 3980763106921604429261768163605691925211349092580537348915200q^{76} \) \(\mathstrut -\mathstrut 26818555005238767738213214331355071802157350668242888658693664q^{77} \) \(\mathstrut -\mathstrut 46918809415480542431744096122363044050717352052893944930893824q^{78} \) \(\mathstrut -\mathstrut 66062584547778855926322557425828318229555831764447318390578800q^{79} \) \(\mathstrut -\mathstrut 24107131515621783296606039111404376381279199126192198883737600q^{80} \) \(\mathstrut +\mathstrut 60169532962747840282744178435382125692147057973395330261005405q^{81} \) \(\mathstrut +\mathstrut 161640005380680171404244248739796231721670355096896899332964352q^{82} \) \(\mathstrut -\mathstrut 11075714578911970422052892182389279259015060887262937688438876q^{83} \) \(\mathstrut +\mathstrut 561576834713135494427720737971974763446026554023921368757698560q^{84} \) \(\mathstrut +\mathstrut 1080977076209142619904291061933013670367861507974853587627651100q^{85} \) \(\mathstrut +\mathstrut 203959478417527130589662521872015124913971020759664996930027520q^{86} \) \(\mathstrut +\mathstrut 2194950060688638911356991860311064353283246752039287494417889880q^{87} \) \(\mathstrut -\mathstrut 634708215367730953097023299586309496019712292081204749934788608q^{88} \) \(\mathstrut -\mathstrut 3808726874831171149148054082536194166490796406679276483013439550q^{89} \) \(\mathstrut +\mathstrut 102744294374853525363014451995526104807175867647866785339801600q^{90} \) \(\mathstrut -\mathstrut 12918162390227545454209872616409212616925919579887907838851122640q^{91} \) \(\mathstrut -\mathstrut 1928904883216743033980111519165472790224951674764104276268548096q^{92} \) \(\mathstrut -\mathstrut 17351070997005472514228954476229969443642401928804118061384220032q^{93} \) \(\mathstrut +\mathstrut 6639539453765509358614844055808459367543338251965312321338736640q^{94} \) \(\mathstrut +\mathstrut 65642393077759635739007960160641202505805759690248833895290471000q^{95} \) \(\mathstrut +\mathstrut 2682584264764440501529820952599581505693943435030653180596715520q^{96} \) \(\mathstrut -\mathstrut 80320521866333789057339919232563862701921173611625715989905231382q^{97} \) \(\mathstrut +\mathstrut 105011570769210578923520629875788498926427144080303889020461514752q^{98} \) \(\mathstrut -\mathstrut 94799615684062844986214986394927237462820082800741591376156914420q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{66}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.66.a.a \(2\) \(53.514\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-8589934592\) \(11\!\cdots\!92\) \(-7\!\cdots\!00\) \(27\!\cdots\!24\) \(+\) \(q-2^{32}q^{2}+(574529980102596-111\beta )q^{3}+\cdots\)
2.66.a.b \(3\) \(53.514\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12884901888\) \(29\!\cdots\!12\) \(39\!\cdots\!50\) \(42\!\cdots\!64\) \(-\) \(q+2^{32}q^{2}+(994852866070404-\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{66}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{66}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{66}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)