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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.24.a.a 1.a 1.a $2$ $3.352$ \(\Q(\sqrt{144169}) \) None \(1080\) \(339480\) \(73069020\) \(-1359184400\) $+$ $\mathrm{SU}(2)$ \(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)