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Properties

Label 3.19
Level 3
Weight 19
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(3))\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.19.b \(\chi_{3}(2, \cdot)\) 3.19.b.a 1 1
3.19.b.b 4