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

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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

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

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 \(-528\) \(-4284\) \(-1025850\) \(3225992\) \(+\) \(q-528q^{2}-4284q^{3}+147712q^{4}+\cdots\)