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

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

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 \(0\) \(15876\) \(0\) \(-95744152\) \(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)