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Properties

Label 3.27
Level 3
Weight 27
Dimension 8
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 27 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(\Gamma_1(3))\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.27.b \(\chi_{3}(2, \cdot)\) 3.27.b.a 8 1