Properties

Label 1.24.a
Level $1$
Weight $24$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(1))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

Trace form

\( 2q + 1080q^{2} + 339480q^{3} + 25326656q^{4} + 73069020q^{5} - 1809673056q^{6} - 1359184400q^{7} + 49459023360q^{8} - 34999394166q^{9} + O(q^{10}) \) \( 2q + 1080q^{2} + 339480q^{3} + 25326656q^{4} + 73069020q^{5} - 1809673056q^{6} - 1359184400q^{7} + 49459023360q^{8} - 34999394166q^{9} - 585013636080q^{10} + 856801968264q^{11} + 2146514952960q^{12} + 4376109322060q^{13} - 41666034529728q^{14} + 42377338985040q^{15} + 15956586401792q^{16} + 254028147597540q^{17} - 695480683916520q^{18} + 4260600979960q^{19} + 250868387468160q^{20} + 1734031637722944q^{21} + 2068343882177760q^{22} - 8144713079008560q^{23} - 1286622315141120q^{24} - 11780274628800850q^{25} + 55025854658735184q^{26} - 5424634982716560q^{27} - 61418438819709440q^{28} + 20818433601623340q^{29} - 155926924188644160q^{30} + 137714017177000384q^{31} + 353265663781601280q^{32} + 68361366766001760q^{33} - 839483655961325328q^{34} + 565961271250425120q^{35} - 1173916300077574848q^{36} - 897721264408967780q^{37} + 5699708971590961440q^{38} - 1785011473665029232q^{39} - 1226668524414336000q^{40} - 2294435477168314956q^{41} - 4657011326437397760q^{42} - 1750760768619855800q^{43} + 12584088840033038592q^{44} + 8897092690294206540q^{45} - 8813206018050221376q^{46} + 15759744217656780960q^{47} - 33749519399576616960q^{48} - 13461981704376200814q^{49} - 51990825483785316600q^{50} + 89998362845078292144q^{51} + 112291883783912022400q^{52} - 140287253401646796420q^{53} + 104731223417039799360q^{54} + 7153550955060182640q^{55} - 232456712054288117760q^{56} - 272752401448627175520q^{57} + 293749486923568689360q^{58} + 280872989971340771880q^{59} + 343522601114937592320q^{60} - 180452892516502223636q^{61} - 540743475843874103040q^{62} + 690775113933935014320q^{63} - 893690254469352914944q^{64} - 632168834809440380760q^{65} - 544338140913651883392q^{66} + 1754233163431557625240q^{67} + 2162050190142944330880q^{68} - 1170560672172404223552q^{69} - 765428657799921252480q^{70} + 3055033510194143328624q^{71} - 4152294352103038548480q^{72} - 8063408253877606149260q^{73} + 6715344283148807757072q^{74} + 190631089350520885800q^{75} + 6207154294513080590080q^{76} - 2165184764357449665600q^{77} + 3614293948840808587200q^{78} + 6244916814559639980640q^{79} - 10840537585501794017280q^{80} - 2793528580929833975598q^{81} - 24457792891615712450640q^{82} + 6875994082418498976120q^{83} + 15917751907190402476032q^{84} + 23969743087870314902520q^{85} - 10916288812918999243296q^{86} - 10026640653837674384880q^{87} + 28988514668199273707520q^{88} + 6395093086173070004820q^{89} - 8986073954327865866160q^{90} - 54890178162704560146016q^{91} - 107907439017191756981760q^{92} + 52900811441357852079360q^{93} + 159400518006534931827072q^{94} - 85533361066700858502000q^{95} + 105592121669584394256384q^{96} - 31147288846254030500540q^{97} + 48364767616374671003640q^{98} - 41158245132312135981912q^{99} + O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.24.a.a \(2\) \(3.352\) \(\Q(\sqrt{144169}) \) None \(1080\) \(339480\) \(73069020\) \(-1359184400\) \(+\) \(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 1080 T - 3691520 T^{2} - 9059696640 T^{3} + 70368744177664 T^{4} \)
$3$ \( 1 - 339480 T + 169266211110 T^{2} - 31959726348189960 T^{3} + \)\(88\!\cdots\!29\)\( T^{4} \)
$5$ \( 1 - 73069020 T + 20480607111358750 T^{2} - \)\(87\!\cdots\!00\)\( T^{3} + \)\(14\!\cdots\!25\)\( T^{4} \)
$7$ \( 1 + 1359184400 T + 35023429308870696750 T^{2} + \)\(37\!\cdots\!00\)\( T^{3} + \)\(74\!\cdots\!49\)\( T^{4} \)
$11$ \( 1 - 856801968264 T + \)\(19\!\cdots\!86\)\( T^{2} - \)\(76\!\cdots\!84\)\( T^{3} + \)\(80\!\cdots\!61\)\( T^{4} \)
$13$ \( 1 - 4376109322060 T + \)\(54\!\cdots\!70\)\( T^{2} - \)\(18\!\cdots\!20\)\( T^{3} + \)\(17\!\cdots\!09\)\( T^{4} \)
$17$ \( 1 - 254028147597540 T + \)\(44\!\cdots\!90\)\( T^{2} - \)\(50\!\cdots\!20\)\( T^{3} + \)\(39\!\cdots\!69\)\( T^{4} \)
$19$ \( 1 - 4260600979960 T + \)\(12\!\cdots\!18\)\( T^{2} - \)\(10\!\cdots\!40\)\( T^{3} + \)\(66\!\cdots\!81\)\( T^{4} \)
$23$ \( 1 + 8144713079008560 T + \)\(58\!\cdots\!30\)\( T^{2} + \)\(17\!\cdots\!20\)\( T^{3} + \)\(43\!\cdots\!89\)\( T^{4} \)
$29$ \( 1 - 20818433601623340 T + \)\(77\!\cdots\!78\)\( T^{2} - \)\(89\!\cdots\!60\)\( T^{3} + \)\(18\!\cdots\!21\)\( T^{4} \)
$31$ \( 1 - 137714017177000384 T + \)\(40\!\cdots\!46\)\( T^{2} - \)\(27\!\cdots\!44\)\( T^{3} + \)\(40\!\cdots\!81\)\( T^{4} \)
$37$ \( 1 + 897721264408967780 T + \)\(19\!\cdots\!70\)\( T^{2} + \)\(10\!\cdots\!40\)\( T^{3} + \)\(13\!\cdots\!09\)\( T^{4} \)
$41$ \( 1 + 2294435477168314956 T + \)\(19\!\cdots\!26\)\( T^{2} + \)\(28\!\cdots\!76\)\( T^{3} + \)\(15\!\cdots\!41\)\( T^{4} \)
$43$ \( 1 + 1750760768619855800 T + \)\(73\!\cdots\!50\)\( T^{2} + \)\(65\!\cdots\!00\)\( T^{3} + \)\(13\!\cdots\!49\)\( T^{4} \)
$47$ \( 1 - 15759744217656780960 T + \)\(36\!\cdots\!10\)\( T^{2} - \)\(45\!\cdots\!80\)\( T^{3} + \)\(82\!\cdots\!29\)\( T^{4} \)
$53$ \( 1 + \)\(14\!\cdots\!20\)\( T + \)\(13\!\cdots\!10\)\( T^{2} + \)\(63\!\cdots\!40\)\( T^{3} + \)\(20\!\cdots\!29\)\( T^{4} \)
$59$ \( 1 - \)\(28\!\cdots\!80\)\( T + \)\(10\!\cdots\!58\)\( T^{2} - \)\(15\!\cdots\!20\)\( T^{3} + \)\(28\!\cdots\!41\)\( T^{4} \)
$61$ \( 1 + \)\(18\!\cdots\!36\)\( T + \)\(96\!\cdots\!86\)\( T^{2} + \)\(20\!\cdots\!16\)\( T^{3} + \)\(13\!\cdots\!61\)\( T^{4} \)
$67$ \( 1 - \)\(17\!\cdots\!40\)\( T + \)\(24\!\cdots\!90\)\( T^{2} - \)\(17\!\cdots\!20\)\( T^{3} + \)\(99\!\cdots\!69\)\( T^{4} \)
$71$ \( 1 - \)\(30\!\cdots\!24\)\( T + \)\(93\!\cdots\!66\)\( T^{2} - \)\(11\!\cdots\!64\)\( T^{3} + \)\(14\!\cdots\!21\)\( T^{4} \)
$73$ \( 1 + \)\(80\!\cdots\!60\)\( T + \)\(30\!\cdots\!30\)\( T^{2} + \)\(57\!\cdots\!20\)\( T^{3} + \)\(51\!\cdots\!89\)\( T^{4} \)
$79$ \( 1 - \)\(62\!\cdots\!40\)\( T + \)\(47\!\cdots\!78\)\( T^{2} - \)\(27\!\cdots\!60\)\( T^{3} + \)\(19\!\cdots\!21\)\( T^{4} \)
$83$ \( 1 - \)\(68\!\cdots\!20\)\( T + \)\(16\!\cdots\!90\)\( T^{2} - \)\(94\!\cdots\!40\)\( T^{3} + \)\(18\!\cdots\!69\)\( T^{4} \)
$89$ \( 1 - \)\(63\!\cdots\!20\)\( T + \)\(13\!\cdots\!38\)\( T^{2} - \)\(43\!\cdots\!80\)\( T^{3} + \)\(46\!\cdots\!61\)\( T^{4} \)
$97$ \( 1 + \)\(31\!\cdots\!40\)\( T + \)\(53\!\cdots\!10\)\( T^{2} + \)\(15\!\cdots\!20\)\( T^{3} + \)\(24\!\cdots\!29\)\( T^{4} \)
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