Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 54 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{54}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 67108864 T )^{2} \))(\( ( 1 - 67108864 T )^{2} \))
$3$ (\( 1 + 1443814773912 T + \)\(25\!\cdots\!82\)\( T^{2} + \)\(27\!\cdots\!76\)\( T^{3} + \)\(37\!\cdots\!29\)\( T^{4} \))(\( 1 + 116235744408 T + \)\(12\!\cdots\!62\)\( T^{2} + \)\(22\!\cdots\!84\)\( T^{3} + \)\(37\!\cdots\!29\)\( T^{4} \))
$5$ (\( 1 - 3028897927064648940 T + \)\(20\!\cdots\!50\)\( T^{2} - \)\(33\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!25\)\( T^{4} \))(\( 1 - 1962806617013976300 T + \)\(22\!\cdots\!50\)\( T^{2} - \)\(21\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!25\)\( T^{4} \))
$7$ (\( 1 + \)\(26\!\cdots\!44\)\( T + \)\(16\!\cdots\!98\)\( T^{2} + \)\(16\!\cdots\!08\)\( T^{3} + \)\(38\!\cdots\!49\)\( T^{4} \))(\( 1 - \)\(71\!\cdots\!04\)\( T + \)\(11\!\cdots\!18\)\( T^{2} - \)\(44\!\cdots\!28\)\( T^{3} + \)\(38\!\cdots\!49\)\( T^{4} \))
$11$ (\( 1 - \)\(73\!\cdots\!24\)\( T + \)\(10\!\cdots\!06\)\( T^{2} - \)\(11\!\cdots\!44\)\( T^{3} + \)\(24\!\cdots\!61\)\( T^{4} \))(\( 1 - \)\(14\!\cdots\!84\)\( T + \)\(30\!\cdots\!26\)\( T^{2} - \)\(21\!\cdots\!04\)\( T^{3} + \)\(24\!\cdots\!61\)\( T^{4} \))
$13$ (\( 1 - \)\(32\!\cdots\!88\)\( T + \)\(15\!\cdots\!42\)\( T^{2} - \)\(35\!\cdots\!64\)\( T^{3} + \)\(11\!\cdots\!09\)\( T^{4} \))(\( 1 + \)\(26\!\cdots\!28\)\( T + \)\(56\!\cdots\!02\)\( T^{2} + \)\(29\!\cdots\!84\)\( T^{3} + \)\(11\!\cdots\!09\)\( T^{4} \))
$17$ (\( 1 - \)\(45\!\cdots\!76\)\( T + \)\(33\!\cdots\!18\)\( T^{2} - \)\(73\!\cdots\!12\)\( T^{3} + \)\(26\!\cdots\!69\)\( T^{4} \))(\( 1 + \)\(61\!\cdots\!36\)\( T + \)\(34\!\cdots\!98\)\( T^{2} + \)\(10\!\cdots\!32\)\( T^{3} + \)\(26\!\cdots\!69\)\( T^{4} \))
$19$ (\( 1 - \)\(80\!\cdots\!00\)\( T + \)\(13\!\cdots\!18\)\( T^{2} - \)\(47\!\cdots\!00\)\( T^{3} + \)\(35\!\cdots\!81\)\( T^{4} \))(\( 1 - \)\(17\!\cdots\!60\)\( T + \)\(16\!\cdots\!18\)\( T^{2} - \)\(10\!\cdots\!40\)\( T^{3} + \)\(35\!\cdots\!81\)\( T^{4} \))
$23$ (\( 1 + \)\(10\!\cdots\!52\)\( T + \)\(29\!\cdots\!42\)\( T^{2} + \)\(15\!\cdots\!16\)\( T^{3} + \)\(22\!\cdots\!89\)\( T^{4} \))(\( 1 - \)\(38\!\cdots\!32\)\( T + \)\(61\!\cdots\!22\)\( T^{2} - \)\(57\!\cdots\!56\)\( T^{3} + \)\(22\!\cdots\!89\)\( T^{4} \))
$29$ (\( 1 - \)\(24\!\cdots\!80\)\( T + \)\(56\!\cdots\!78\)\( T^{2} - \)\(77\!\cdots\!20\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 - \)\(70\!\cdots\!00\)\( T + \)\(53\!\cdots\!78\)\( T^{2} - \)\(22\!\cdots\!00\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))
$31$ (\( 1 - \)\(14\!\cdots\!04\)\( T + \)\(20\!\cdots\!86\)\( T^{2} - \)\(15\!\cdots\!64\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 - \)\(25\!\cdots\!24\)\( T + \)\(18\!\cdots\!26\)\( T^{2} - \)\(27\!\cdots\!84\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))
$37$ (\( 1 + \)\(49\!\cdots\!24\)\( T + \)\(18\!\cdots\!38\)\( T^{2} + \)\(64\!\cdots\!28\)\( T^{3} + \)\(16\!\cdots\!09\)\( T^{4} \))(\( 1 - \)\(98\!\cdots\!64\)\( T + \)\(48\!\cdots\!18\)\( T^{2} - \)\(12\!\cdots\!08\)\( T^{3} + \)\(16\!\cdots\!09\)\( T^{4} \))
$41$ (\( 1 + \)\(11\!\cdots\!76\)\( T + \)\(83\!\cdots\!86\)\( T^{2} + \)\(34\!\cdots\!96\)\( T^{3} + \)\(90\!\cdots\!41\)\( T^{4} \))(\( 1 - \)\(10\!\cdots\!04\)\( T + \)\(67\!\cdots\!46\)\( T^{2} - \)\(31\!\cdots\!84\)\( T^{3} + \)\(90\!\cdots\!41\)\( T^{4} \))
$43$ (\( 1 + \)\(59\!\cdots\!52\)\( T + \)\(16\!\cdots\!62\)\( T^{2} + \)\(22\!\cdots\!36\)\( T^{3} + \)\(14\!\cdots\!49\)\( T^{4} \))(\( 1 - \)\(21\!\cdots\!92\)\( T + \)\(59\!\cdots\!02\)\( T^{2} - \)\(79\!\cdots\!56\)\( T^{3} + \)\(14\!\cdots\!49\)\( T^{4} \))
$47$ (\( 1 - \)\(11\!\cdots\!56\)\( T + \)\(22\!\cdots\!38\)\( T^{2} - \)\(46\!\cdots\!12\)\( T^{3} + \)\(17\!\cdots\!29\)\( T^{4} \))(\( 1 - \)\(15\!\cdots\!04\)\( T + \)\(89\!\cdots\!58\)\( T^{2} - \)\(65\!\cdots\!08\)\( T^{3} + \)\(17\!\cdots\!29\)\( T^{4} \))
$53$ (\( 1 - \)\(21\!\cdots\!08\)\( T + \)\(47\!\cdots\!62\)\( T^{2} - \)\(52\!\cdots\!84\)\( T^{3} + \)\(59\!\cdots\!29\)\( T^{4} \))(\( 1 + \)\(51\!\cdots\!48\)\( T + \)\(41\!\cdots\!22\)\( T^{2} + \)\(12\!\cdots\!04\)\( T^{3} + \)\(59\!\cdots\!29\)\( T^{4} \))
$59$ (\( 1 + \)\(25\!\cdots\!40\)\( T + \)\(30\!\cdots\!58\)\( T^{2} + \)\(18\!\cdots\!60\)\( T^{3} + \)\(51\!\cdots\!41\)\( T^{4} \))(\( 1 - \)\(69\!\cdots\!00\)\( T + \)\(12\!\cdots\!58\)\( T^{2} - \)\(49\!\cdots\!00\)\( T^{3} + \)\(51\!\cdots\!41\)\( T^{4} \))
$61$ (\( 1 + \)\(36\!\cdots\!96\)\( T + \)\(11\!\cdots\!66\)\( T^{2} + \)\(15\!\cdots\!76\)\( T^{3} + \)\(17\!\cdots\!61\)\( T^{4} \))(\( 1 - \)\(10\!\cdots\!44\)\( T + \)\(76\!\cdots\!46\)\( T^{2} - \)\(44\!\cdots\!64\)\( T^{3} + \)\(17\!\cdots\!61\)\( T^{4} \))
$67$ (\( 1 - \)\(31\!\cdots\!36\)\( T + \)\(27\!\cdots\!98\)\( T^{2} - \)\(18\!\cdots\!32\)\( T^{3} + \)\(36\!\cdots\!69\)\( T^{4} \))(\( 1 + \)\(54\!\cdots\!56\)\( T + \)\(18\!\cdots\!58\)\( T^{2} + \)\(32\!\cdots\!72\)\( T^{3} + \)\(36\!\cdots\!69\)\( T^{4} \))
$71$ (\( 1 + \)\(13\!\cdots\!36\)\( T + \)\(30\!\cdots\!46\)\( T^{2} + \)\(17\!\cdots\!96\)\( T^{3} + \)\(17\!\cdots\!21\)\( T^{4} \))(\( 1 + \)\(17\!\cdots\!96\)\( T + \)\(26\!\cdots\!26\)\( T^{2} + \)\(23\!\cdots\!56\)\( T^{3} + \)\(17\!\cdots\!21\)\( T^{4} \))
$73$ (\( 1 + \)\(15\!\cdots\!32\)\( T + \)\(11\!\cdots\!22\)\( T^{2} + \)\(88\!\cdots\!56\)\( T^{3} + \)\(32\!\cdots\!89\)\( T^{4} \))(\( 1 - \)\(50\!\cdots\!92\)\( T + \)\(10\!\cdots\!82\)\( T^{2} - \)\(28\!\cdots\!36\)\( T^{3} + \)\(32\!\cdots\!89\)\( T^{4} \))
$79$ (\( 1 + \)\(48\!\cdots\!80\)\( T + \)\(11\!\cdots\!78\)\( T^{2} + \)\(18\!\cdots\!20\)\( T^{3} + \)\(14\!\cdots\!21\)\( T^{4} \))(\( 1 + \)\(44\!\cdots\!20\)\( T + \)\(45\!\cdots\!78\)\( T^{2} + \)\(16\!\cdots\!80\)\( T^{3} + \)\(14\!\cdots\!21\)\( T^{4} \))
$83$ (\( 1 - \)\(56\!\cdots\!08\)\( T + \)\(10\!\cdots\!42\)\( T^{2} - \)\(28\!\cdots\!04\)\( T^{3} + \)\(26\!\cdots\!69\)\( T^{4} \))(\( 1 + \)\(11\!\cdots\!08\)\( T + \)\(13\!\cdots\!42\)\( T^{2} + \)\(61\!\cdots\!04\)\( T^{3} + \)\(26\!\cdots\!69\)\( T^{4} \))
$89$ (\( 1 - \)\(27\!\cdots\!80\)\( T + \)\(11\!\cdots\!38\)\( T^{2} - \)\(58\!\cdots\!20\)\( T^{3} + \)\(43\!\cdots\!61\)\( T^{4} \))(\( 1 + \)\(77\!\cdots\!20\)\( T + \)\(43\!\cdots\!38\)\( T^{2} + \)\(16\!\cdots\!80\)\( T^{3} + \)\(43\!\cdots\!61\)\( T^{4} \))
$97$ (\( 1 - \)\(13\!\cdots\!16\)\( T + \)\(39\!\cdots\!18\)\( T^{2} - \)\(27\!\cdots\!32\)\( T^{3} + \)\(39\!\cdots\!29\)\( T^{4} \))(\( 1 - \)\(10\!\cdots\!84\)\( T + \)\(60\!\cdots\!18\)\( T^{2} - \)\(20\!\cdots\!68\)\( T^{3} + \)\(39\!\cdots\!29\)\( T^{4} \))
show more
show less