Properties

Label 3.19.b
Level 3
Weight 19
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(3, [\chi])\).

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

Trace form

\( 5q - 3807q^{3} - 791392q^{4} + 22698144q^{6} - 18194966q^{7} - 497920851q^{9} + O(q^{10}) \) \( 5q - 3807q^{3} - 791392q^{4} + 22698144q^{6} - 18194966q^{7} - 497920851q^{9} + 1461136320q^{10} + 1963390752q^{12} - 12623763374q^{13} - 68287821120q^{15} + 269943484928q^{16} - 624067623360q^{18} + 499976330338q^{19} - 2369900042334q^{21} + 6661732766400q^{22} - 16917300997632q^{24} + 15222296719805q^{25} - 12257805176343q^{27} + 26079914794816q^{28} - 17181499602240q^{30} - 14290577087750q^{31} + 12242871023040q^{33} - 97283346838272q^{34} + 514217410690464q^{36} - 498540780532286q^{37} + 558578761159914q^{39} - 967003294602240q^{40} + 149151729948480q^{42} + 869221682027506q^{43} - 221242601301120q^{45} + 571461969379968q^{46} - 3545430525937152q^{48} + 961675207023903q^{49} - 4987666703736576q^{51} + 17957128687741504q^{52} - 14022277970462496q^{54} - 84999034592640q^{55} + 4095971428136634q^{57} - 15931261886420160q^{58} + 24723268055608320q^{60} - 11694429845800910q^{61} + 43877326387255866q^{63} - 35478969080111104q^{64} + 14857554290281920q^{66} - 83078831080537406q^{67} + 81420525478583424q^{69} + 4599036429482880q^{70} - 4994921842560000q^{72} - 75298953006735974q^{73} - 18571774769913735q^{75} + 425674981848697408q^{76} - 685829939469704640q^{78} - 36709816528688102q^{79} + 77312107424281365q^{81} + 887840438080579200q^{82} - 525824181721215936q^{84} - 258438267155888640q^{85} + 858898556077746240q^{87} - 494740797131842560q^{88} - 688243478411603520q^{90} - 1183285654493642908q^{91} + 1803351257715032946q^{93} + 1164172551956805888q^{94} + 1176359757688184832q^{96} - 3350690566618697846q^{97} + 3027708259671116160q^{99} + O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.19.b.a \(1\) \(6.162\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-19683\) \(0\) \(77549186\) \(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b \(4\) \(6.162\) 4.0.601940665.1 None \(0\) \(15876\) \(0\) \(-95744152\) \(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)