Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 24 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

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 \(1080\) \(339480\) \(73069020\) \(-1359184400\) \(+\) \(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)