Properties

Label 3.27.b
Level 3
Weight 27
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 27 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(3, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 8 8 0
Eisenstein series 2 2 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 1261080q^{3} \) \(\mathstrut -\mathstrut 248848672q^{4} \) \(\mathstrut +\mathstrut 4268261088q^{6} \) \(\mathstrut -\mathstrut 83723264240q^{7} \) \(\mathstrut +\mathstrut 3535237525320q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 1261080q^{3} \) \(\mathstrut -\mathstrut 248848672q^{4} \) \(\mathstrut +\mathstrut 4268261088q^{6} \) \(\mathstrut -\mathstrut 83723264240q^{7} \) \(\mathstrut +\mathstrut 3535237525320q^{9} \) \(\mathstrut -\mathstrut 19160376580800q^{10} \) \(\mathstrut +\mathstrut 361652147111520q^{12} \) \(\mathstrut -\mathstrut 397915354631600q^{13} \) \(\mathstrut -\mathstrut 719893807027200q^{15} \) \(\mathstrut +\mathstrut 14708338775335424q^{16} \) \(\mathstrut -\mathstrut 21900893760832320q^{18} \) \(\mathstrut +\mathstrut 16320401555362000q^{19} \) \(\mathstrut +\mathstrut 194580840365988048q^{21} \) \(\mathstrut -\mathstrut 772248680481769920q^{22} \) \(\mathstrut -\mathstrut 462343148304920064q^{24} \) \(\mathstrut +\mathstrut 1971388854053049800q^{25} \) \(\mathstrut -\mathstrut 7894649015962792920q^{27} \) \(\mathstrut +\mathstrut 15321751531929304000q^{28} \) \(\mathstrut +\mathstrut 7398480599799681600q^{30} \) \(\mathstrut -\mathstrut 9272518953250081904q^{31} \) \(\mathstrut -\mathstrut 65168600178932490240q^{33} \) \(\mathstrut +\mathstrut 221246262521511042816q^{34} \) \(\mathstrut -\mathstrut 1016435634925989724704q^{36} \) \(\mathstrut +\mathstrut 879374467120740709840q^{37} \) \(\mathstrut -\mathstrut 1582238541124790450928q^{39} \) \(\mathstrut +\mathstrut 4129217584783179033600q^{40} \) \(\mathstrut -\mathstrut 6703469261814514512960q^{42} \) \(\mathstrut +\mathstrut 6748593942335676212560q^{43} \) \(\mathstrut -\mathstrut 16831420952659929907200q^{45} \) \(\mathstrut +\mathstrut 36160927581299221074816q^{46} \) \(\mathstrut -\mathstrut 66488551077760679646720q^{48} \) \(\mathstrut +\mathstrut 45841873858091621647512q^{49} \) \(\mathstrut -\mathstrut 62114113806050924347392q^{51} \) \(\mathstrut +\mathstrut 99815113130579384624320q^{52} \) \(\mathstrut -\mathstrut 65423424830500017302112q^{54} \) \(\mathstrut +\mathstrut 31541176921532063385600q^{55} \) \(\mathstrut -\mathstrut 68601650728105742286960q^{57} \) \(\mathstrut +\mathstrut 179274146475296123858880q^{58} \) \(\mathstrut +\mathstrut 132515345363297827507200q^{60} \) \(\mathstrut -\mathstrut 319050283467071524566704q^{61} \) \(\mathstrut +\mathstrut 658789337835295522626960q^{63} \) \(\mathstrut -\mathstrut 1937027849517856838066176q^{64} \) \(\mathstrut +\mathstrut 3327191890146340029253440q^{66} \) \(\mathstrut -\mathstrut 3016122636770760226629680q^{67} \) \(\mathstrut +\mathstrut 2874694883813365556256768q^{69} \) \(\mathstrut -\mathstrut 3079956143630742638371200q^{70} \) \(\mathstrut +\mathstrut 4816528692447953902187520q^{72} \) \(\mathstrut -\mathstrut 1734362529074066854728560q^{73} \) \(\mathstrut +\mathstrut 551279759153288953055400q^{75} \) \(\mathstrut -\mathstrut 4252629668197637559664448q^{76} \) \(\mathstrut -\mathstrut 2905541033044787133422400q^{78} \) \(\mathstrut +\mathstrut 5851464318766097144790160q^{79} \) \(\mathstrut -\mathstrut 7387002303358032367832952q^{81} \) \(\mathstrut +\mathstrut 19281076716095151109326720q^{82} \) \(\mathstrut -\mathstrut 58831332525651421466918208q^{84} \) \(\mathstrut +\mathstrut 36766362882842005714329600q^{85} \) \(\mathstrut -\mathstrut 66105320167985812595481600q^{87} \) \(\mathstrut +\mathstrut 166743215953906759732730880q^{88} \) \(\mathstrut -\mathstrut 112582289830354559315755200q^{90} \) \(\mathstrut +\mathstrut 57658591275235919126596256q^{91} \) \(\mathstrut -\mathstrut 721851591602497641585840q^{93} \) \(\mathstrut -\mathstrut 128592383810221185199398144q^{94} \) \(\mathstrut +\mathstrut 66451111218720743421763584q^{96} \) \(\mathstrut +\mathstrut 87088434574088023884109840q^{97} \) \(\mathstrut +\mathstrut 126385397236902706353285120q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{27}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.27.b.a \(8\) \(12.849\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-1261080\) \(0\) \(-83723264240\) \(q+\beta _{1}q^{2}+(-157635-5\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)