# Properties

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

# Related objects

## 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: $$\Q$$ Newform subspaces: $$2$$ 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

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

## Decomposition of $$S_{19}^{\mathrm{new}}(3, [\chi])$$ into newform subspaces

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