# Properties

 Label 38.5.f Level $38$ Weight $5$ Character orbit 38.f Rep. character $\chi_{38}(3,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $36$ Newform subspaces $1$ Sturm bound $25$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$38 = 2 \cdot 19$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 38.f (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$1$$ Sturm bound: $$25$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(38, [\chi])$$.

Total New Old
Modular forms 132 36 96
Cusp forms 108 36 72
Eisenstein series 24 0 24

## Trace form

 $$36q + 12q^{3} + 48q^{6} + 90q^{7} - 84q^{9} + O(q^{10})$$ $$36q + 12q^{3} + 48q^{6} + 90q^{7} - 84q^{9} + 90q^{11} - 432q^{12} - 330q^{13} + 576q^{14} + 2658q^{15} - 522q^{17} - 1236q^{19} - 864q^{20} - 1998q^{21} - 1344q^{22} - 1440q^{23} - 384q^{24} - 3276q^{25} + 576q^{26} + 1692q^{27} + 1056q^{28} + 4050q^{29} + 2808q^{31} + 2910q^{33} + 1536q^{34} + 1422q^{35} + 672q^{36} + 1872q^{38} - 9024q^{39} - 3060q^{41} - 3456q^{42} - 1218q^{43} - 5760q^{44} - 2592q^{45} - 2880q^{46} + 990q^{47} + 1536q^{48} - 9696q^{49} + 27648q^{50} + 35784q^{51} - 1488q^{52} + 17082q^{53} + 2160q^{54} + 4290q^{55} + 204q^{57} - 5376q^{58} - 11142q^{59} - 11856q^{60} - 35928q^{61} - 7200q^{62} - 58254q^{63} + 9216q^{64} - 34290q^{65} - 32928q^{66} + 44322q^{67} - 4752q^{68} + 21762q^{69} + 12864q^{70} + 40428q^{71} + 10752q^{72} + 6936q^{73} - 4032q^{74} - 576q^{76} - 36648q^{77} - 11040q^{78} - 29298q^{79} + 24324q^{81} - 14592q^{82} + 23958q^{83} + 36720q^{84} + 2772q^{85} + 30816q^{86} + 14256q^{87} + 26064q^{89} + 14784q^{90} + 100044q^{91} + 9360q^{92} + 26400q^{93} - 38646q^{95} - 55746q^{97} - 64512q^{98} - 69846q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(38, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
38.5.f.a $$36$$ $$3.928$$ None $$0$$ $$12$$ $$0$$ $$90$$

## Decomposition of $$S_{5}^{\mathrm{old}}(38, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(38, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 2}$$