Properties

Label 2.54.a
Level 2
Weight 54
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 13
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 54 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{54}(\Gamma_0(2))\).

Total New Old
Modular forms 14 4 10
Cusp forms 12 4 8
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.
\(+\)\(2\)
\(-\)\(2\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 1560050518320q^{3} \) \(\mathstrut +\mathstrut 18014398509481984q^{4} \) \(\mathstrut +\mathstrut 4991704544078625240q^{5} \) \(\mathstrut +\mathstrut 89092320540235923456q^{6} \) \(\mathstrut -\mathstrut 19520756791511146188640q^{7} \) \(\mathstrut +\mathstrut 2776022908307280883876212q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 1560050518320q^{3} \) \(\mathstrut +\mathstrut 18014398509481984q^{4} \) \(\mathstrut +\mathstrut 4991704544078625240q^{5} \) \(\mathstrut +\mathstrut 89092320540235923456q^{6} \) \(\mathstrut -\mathstrut 19520756791511146188640q^{7} \) \(\mathstrut +\mathstrut 2776022908307280883876212q^{9} \) \(\mathstrut -\mathstrut 71544176737772423306280960q^{10} \) \(\mathstrut +\mathstrut 2142694537910661648503204208q^{11} \) \(\mathstrut -\mathstrut 7025842932985101143475486720q^{12} \) \(\mathstrut +\mathstrut 60344027666455979343009290360q^{13} \) \(\mathstrut +\mathstrut 2270506340305585224308723023872q^{14} \) \(\mathstrut -\mathstrut 6201420836088064937333577899040q^{15} \) \(\mathstrut +\mathstrut 81129638414606681695789005144064q^{16} \) \(\mathstrut +\mathstrut 390814645082473152103643455604040q^{17} \) \(\mathstrut +\mathstrut 1629134981364474869731216211312640q^{18} \) \(\mathstrut +\mathstrut 25929116929850635447041389195782160q^{19} \) \(\mathstrut +\mathstrut 22480638724656108256299739816919040q^{20} \) \(\mathstrut +\mathstrut 394771895779594321867674270832414848q^{21} \) \(\mathstrut +\mathstrut 45130739230028225099668455570800640q^{22} \) \(\mathstrut -\mathstrut 633214468289510915651385655852415520q^{23} \) \(\mathstrut +\mathstrut 401236141586579291759317399608754176q^{24} \) \(\mathstrut -\mathstrut 28491045542470319250442129830422648900q^{25} \) \(\mathstrut -\mathstrut 39844132752565985540847754416670900224q^{26} \) \(\mathstrut -\mathstrut 7809985942206692308462718091600323040q^{27} \) \(\mathstrut -\mathstrut 87913673012239677049729289255586365440q^{28} \) \(\mathstrut +\mathstrut 944044275331789353730705604238161367480q^{29} \) \(\mathstrut +\mathstrut 1773937712802897717735712483147996200960q^{30} \) \(\mathstrut +\mathstrut 3953080275315069244491977760757304486528q^{31} \) \(\mathstrut -\mathstrut 24209322374612114580791637104452402294080q^{33} \) \(\mathstrut -\mathstrut 34433261183360791180350474382814969069568q^{34} \) \(\mathstrut -\mathstrut 146255815252668079291735458589805762172480q^{35} \) \(\mathstrut +\mathstrut 12502095735424630773445353015725525041152q^{36} \) \(\mathstrut +\mathstrut 492508919967712252044646617391320701258840q^{37} \) \(\mathstrut +\mathstrut 664190267827962746509997714622118090506240q^{38} \) \(\mathstrut +\mathstrut 1884091754337154303259669704999162182847584q^{39} \) \(\mathstrut -\mathstrut 322206327696760793717690769958485790556160q^{40} \) \(\mathstrut -\mathstrut 987450320870308137257392295344698403347672q^{41} \) \(\mathstrut -\mathstrut 10868299736413494634357330136880509374955520q^{42} \) \(\mathstrut -\mathstrut 37936471017722016868832473148242575302022160q^{43} \) \(\mathstrut +\mathstrut 9649838322503252915039984077577473562247168q^{44} \) \(\mathstrut +\mathstrut 16207580024064231799949544585786593451590520q^{45} \) \(\mathstrut +\mathstrut 94159536480170052385665905337585087415320576q^{46} \) \(\mathstrut +\mathstrut 268620141179625291035662644033627066223642560q^{47} \) \(\mathstrut -\mathstrut 31641583614955334209612723509088547367813120q^{48} \) \(\mathstrut +\mathstrut 663810376372716243669042008936102286971675748q^{49} \) \(\mathstrut -\mathstrut 541029793809247683193194243488800204809830400q^{50} \) \(\mathstrut -\mathstrut 4408316667475663900013451768157093231702876512q^{51} \) \(\mathstrut +\mathstrut 271765340512686049855407619645498265761218560q^{52} \) \(\mathstrut -\mathstrut 2994398646521939416793808509993339915216667240q^{53} \) \(\mathstrut -\mathstrut 94698267705193441577371371727926772598046720q^{54} \) \(\mathstrut +\mathstrut 21982452772861378412663227241058636445378853280q^{55} \) \(\mathstrut +\mathstrut 10225451508142582199271334446421735941196480512q^{56} \) \(\mathstrut +\mathstrut 39151644212770112714718092889598220322124004160q^{57} \) \(\mathstrut +\mathstrut 31103043011876269304255824872951536694885089280q^{58} \) \(\mathstrut -\mathstrut 188793722028256056952659869681129991419440466640q^{59} \) \(\mathstrut -\mathstrut 27928716566573839005014563507714328935362723840q^{60} \) \(\mathstrut -\mathstrut 256733469449441068784788756088145078366904593352q^{61} \) \(\mathstrut +\mathstrut 71103449639500897738096973428483267390372577280q^{62} \) \(\mathstrut -\mathstrut 195889792434056826178984597004691575119663519200q^{63} \) \(\mathstrut +\mathstrut 365375409332725729550921208179070754913983135744q^{64} \) \(\mathstrut +\mathstrut 2256731164367287232951175759235994456365141415760q^{65} \) \(\mathstrut +\mathstrut 2942942567716744598404510507019761240022043328512q^{66} \) \(\mathstrut -\mathstrut 5087773231159770666202657923754787906796110390320q^{67} \) \(\mathstrut +\mathstrut 1760072689964358734795958904961137089420554403840q^{68} \) \(\mathstrut -\mathstrut 11276378740046241845129058911505500976757424946816q^{69} \) \(\mathstrut +\mathstrut 13825681140616259316665894889099044149310018027520q^{70} \) \(\mathstrut -\mathstrut 31570310753561750455489443603946095588708306049632q^{71} \) \(\mathstrut +\mathstrut 7336971695009288968427991400859895365811767869440q^{72} \) \(\mathstrut -\mathstrut 10453867118107682453710090716258375539138629796440q^{73} \) \(\mathstrut +\mathstrut 99516699190362943963495544205392558150675104530432q^{74} \) \(\mathstrut -\mathstrut 14285230286929711953786583696473699678146510619600q^{75} \) \(\mathstrut +\mathstrut 116774361343321341071050519666273412280734827151360q^{76} \) \(\mathstrut -\mathstrut 304432477138196478109050350470521703663029979858560q^{77} \) \(\mathstrut +\mathstrut 458706075410391326107761310545188726403277950812160q^{78} \) \(\mathstrut -\mathstrut 526902450967932653030544240962281421917797238091200q^{79} \) \(\mathstrut +\mathstrut 101243796183411991571273318124199665236407316643840q^{80} \) \(\mathstrut -\mathstrut 1350454660495109121656710431487630302798705783878556q^{81} \) \(\mathstrut +\mathstrut 1476765553805464442291662200962654780193983346769920q^{82} \) \(\mathstrut -\mathstrut 624914484518803492002020274809800202184329670505200q^{83} \) \(\mathstrut +\mathstrut 1777894562729325270473332367353046335608388067524608q^{84} \) \(\mathstrut -\mathstrut 1225374125445778632210010338207066818555783881859280q^{85} \) \(\mathstrut +\mathstrut 5386758954157914551145421820455165203417214343970816q^{86} \) \(\mathstrut -\mathstrut 2881229669664619941655023270936625640201242418885280q^{87} \) \(\mathstrut +\mathstrut 203250780379310140120107431618850598510520633917440q^{88} \) \(\mathstrut -\mathstrut 4978861569931693766833921952294855287581951654364440q^{89} \) \(\mathstrut +\mathstrut 534396672330018460219880778664446486004769929297920q^{90} \) \(\mathstrut -\mathstrut 17121428812830427262737992276003778964042932285443392q^{91} \) \(\mathstrut -\mathstrut 2851744443434248115383399537935264682871707580497920q^{92} \) \(\mathstrut +\mathstrut 10111529951962266813133344031337089348683944732090880q^{93} \) \(\mathstrut +\mathstrut 3091763126082963902579048465217213969811605471363072q^{94} \) \(\mathstrut +\mathstrut 46141603537726751531749413774126677112285999221954400q^{95} \) \(\mathstrut +\mathstrut 1807006937736894072086447295932255312253737339191296q^{96} \) \(\mathstrut +\mathstrut 115117497627022096191803064584240888515903225493381000q^{97} \) \(\mathstrut -\mathstrut 171665842451372939598486430983163619169159971749232640q^{98} \) \(\mathstrut +\mathstrut 52785965099088048923130040705546856037606566391893424q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{54}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.54.a.a \(2\) \(35.581\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-134217728\) \(-1\!\cdots\!12\) \(30\!\cdots\!40\) \(-2\!\cdots\!44\) \(+\) \(q-2^{26}q^{2}+(-721907386956-3\beta )q^{3}+\cdots\)
2.54.a.b \(2\) \(35.581\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(134217728\) \(-116235744408\) \(19\!\cdots\!00\) \(71\!\cdots\!04\) \(-\) \(q+2^{26}q^{2}+(-58117872204-\beta )q^{3}+\cdots\)

Decomposition of \(S_{54}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{54}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{54}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)