Properties

Label 1.18.a
Level 1
Weight 18
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 1
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(1))\).

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

Trace form

\( q - 528q^{2} - 4284q^{3} + 147712q^{4} - 1025850q^{5} + 2261952q^{6} + 3225992q^{7} - 8785920q^{8} - 110787507q^{9} + O(q^{10}) \) \( q - 528q^{2} - 4284q^{3} + 147712q^{4} - 1025850q^{5} + 2261952q^{6} + 3225992q^{7} - 8785920q^{8} - 110787507q^{9} + 541648800q^{10} - 753618228q^{11} - 632798208q^{12} + 2541064526q^{13} - 1703323776q^{14} + 4394741400q^{15} - 14721941504q^{16} - 5429742318q^{17} + 58495803696q^{18} + 1487499860q^{19} - 151530355200q^{20} - 13820149728q^{21} + 397910424384q^{22} - 317091823464q^{23} + 37638881280q^{24} + 289428769375q^{25} - 1341682069728q^{26} + 1027850138280q^{27} + 476517730304q^{28} + 2433410602590q^{29} - 2320423459200q^{30} - 8849722053088q^{31} + 8924773220352q^{32} + 3228500488752q^{33} + 2866903943904q^{34} - 3309383893200q^{35} - 16364644233984q^{36} + 12691652946662q^{37} - 785399926080q^{38} - 10885920429384q^{39} + 9013036032000q^{40} + 48864151002282q^{41} + 7297039056384q^{42} - 91019974317844q^{43} - 111318455694336q^{44} + 113651364055950q^{45} + 167424482788992q^{46} - 49304994276048q^{47} + 63068797403136q^{48} - 222223489603143q^{49} - 152818390230000q^{50} + 23261016090312q^{51} + 375345723264512q^{52} + 22940453195766q^{53} - 542704873011840q^{54} + 773099259193800q^{55} - 28343307632640q^{56} - 6372449400240q^{57} - 1284840798167520q^{58} + 32695090729980q^{59} + 649156041676800q^{60} - 1308285854869378q^{61} + 4672653244030464q^{62} - 357399611281944q^{63} - 2782645943533568q^{64} - 2606751043997100q^{65} - 1704648258061056q^{66} + 5196143861984132q^{67} - 802038097276416q^{68} + 1358421371719776q^{69} + 1747354695609600q^{70} - 3709489877412408q^{71} + 973370173501440q^{72} + 3402372968272586q^{73} - 6701192755837536q^{74} - 1239912848002500q^{75} + 219721579320320q^{76} - 2431166374582176q^{77} + 5747765986714752q^{78} + 2366533941308240q^{79} + 15102503691878400q^{80} + 9903806719952121q^{81} - 25800271729204896q^{82} - 29766750443172204q^{83} - 2041401956622336q^{84} + 5570101156920300q^{85} + 48058546439821632q^{86} - 10424731021495560q^{87} + 6621229461749760q^{88} + 29167184100574170q^{89} - 60007920221541600q^{90} + 8197453832359792q^{91} - 46838267427514368q^{92} + 37912209275428992q^{93} + 26033036977753344q^{94} - 1525951731381000q^{95} - 38233728475987968q^{96} - 63769879140957598q^{97} + 117334002510459504q^{98} + 83491484709877596q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.18.a.a \(1\) \(1.832\) \(\Q\) None \(-528\) \(-4284\) \(-1025850\) \(3225992\) \(+\) \(q-528q^{2}-4284q^{3}+147712q^{4}+\cdots\)