# Properties

 Label 38.2.c Level $38$ Weight $2$ Character orbit 38.c Rep. character $\chi_{38}(7,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $2$ Sturm bound $10$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$38 = 2 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 38.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(38, [\chi])$$.

Total New Old
Modular forms 14 6 8
Cusp forms 6 6 0
Eisenstein series 8 0 8

## Trace form

 $$6 q - q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - 6 q^{9} + O(q^{10})$$ $$6 q - q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 6 q^{14} + 14 q^{15} - 3 q^{16} + 6 q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{20} - 10 q^{21} + 7 q^{22} + 4 q^{23} + q^{24} - q^{25} + 4 q^{26} - 10 q^{27} + 2 q^{28} + 2 q^{29} - 28 q^{30} - 8 q^{31} - q^{32} + 11 q^{33} - 6 q^{34} + 12 q^{35} - 6 q^{36} - 8 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 19 q^{41} - 18 q^{42} - 8 q^{43} + q^{44} + 16 q^{45} + 16 q^{46} - 14 q^{47} - q^{48} + 22 q^{49} + 22 q^{50} + 6 q^{51} - 6 q^{52} - 2 q^{53} - 5 q^{54} - 10 q^{55} + 12 q^{56} + 36 q^{57} - 4 q^{58} + 9 q^{59} + 14 q^{60} + 18 q^{61} + 8 q^{62} - 16 q^{63} + 6 q^{64} + 8 q^{65} + 17 q^{66} + 11 q^{67} - 12 q^{68} - 40 q^{69} + 12 q^{70} + 22 q^{71} - 10 q^{72} - 13 q^{73} - 16 q^{74} - 66 q^{75} - 13 q^{76} - 60 q^{77} + 2 q^{78} + 12 q^{79} - 2 q^{80} + 9 q^{81} - q^{82} + 6 q^{83} + 20 q^{84} - 16 q^{86} + 28 q^{87} - 14 q^{88} - 6 q^{89} - 8 q^{90} + 4 q^{91} + 4 q^{92} + 12 q^{93} + 28 q^{94} - 28 q^{95} - 2 q^{96} + q^{97} + 7 q^{98} + 22 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(38, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.2.c.a $2$ $0.303$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-8$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
38.2.c.b $4$ $0.303$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$-2$$ $$0$$ $$-2$$ $$4$$ $$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$