# Properties

 Label 38.8.c Level $38$ Weight $8$ Character orbit 38.c Rep. character $\chi_{38}(7,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $26$ Newform subspaces $2$ Sturm bound $40$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$38 = 2 \cdot 19$$ Weight: $$k$$ $$=$$ $$8$$ 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: $$40$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(38, [\chi])$$.

Total New Old
Modular forms 74 26 48
Cusp forms 66 26 40
Eisenstein series 8 0 8

## Trace form

 $$26q + 8q^{2} + 67q^{3} - 832q^{4} - 2q^{5} - 344q^{6} + 892q^{7} - 1024q^{8} - 11834q^{9} + O(q^{10})$$ $$26q + 8q^{2} + 67q^{3} - 832q^{4} - 2q^{5} - 344q^{6} + 892q^{7} - 1024q^{8} - 11834q^{9} + 2000q^{10} - 11114q^{11} - 8576q^{12} + 16082q^{13} + 11856q^{14} + 4678q^{15} - 53248q^{16} + 55782q^{17} + 42080q^{18} - 113727q^{19} + 256q^{20} + 15450q^{21} + 49624q^{22} - 37268q^{23} - 22016q^{24} - 283611q^{25} - 299168q^{26} + 226510q^{27} - 28544q^{28} + 277514q^{29} + 204832q^{30} - 165224q^{31} + 32768q^{32} + 326993q^{33} + 277808q^{34} - 564612q^{35} - 757376q^{36} + 1303064q^{37} + 133696q^{38} - 1296876q^{39} + 128000q^{40} + 555443q^{41} + 612944q^{42} + 2507656q^{43} + 355648q^{44} - 3398656q^{45} - 3046016q^{46} - 2194838q^{47} + 274432q^{48} + 5995178q^{49} + 2933200q^{50} + 4784254q^{51} + 1029248q^{52} + 1101694q^{53} - 3465224q^{54} - 2775962q^{55} - 1517568q^{56} - 2714088q^{57} + 926368q^{58} + 28797q^{59} + 299392q^{60} - 3392246q^{61} + 2275136q^{62} - 851888q^{63} + 6815744q^{64} + 9127808q^{65} - 3423624q^{66} - 3547953q^{67} - 7140096q^{68} - 24724432q^{69} - 3986208q^{70} + 4497358q^{71} - 1346560q^{72} + 5721781q^{73} - 2164864q^{74} - 12783786q^{75} + 63936q^{76} - 11604420q^{77} + 16224016q^{78} + 799284q^{79} - 8192q^{80} - 10123481q^{81} + 3382728q^{82} + 17700078q^{83} - 1977600q^{84} + 25388772q^{85} + 8436224q^{86} + 40339436q^{87} - 6351872q^{88} + 16795458q^{89} + 17026112q^{90} - 33000876q^{91} - 2385152q^{92} - 31032284q^{93} - 40843808q^{94} + 22424876q^{95} + 2818048q^{96} - 18311673q^{97} + 23210056q^{98} + 26293582q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(38, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
38.8.c.a $$12$$ $$11.871$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-48$$ $$12$$ $$124$$ $$-1036$$ $$q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots$$
38.8.c.b $$14$$ $$11.871$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$56$$ $$55$$ $$-126$$ $$1928$$ $$q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(38, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(38, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 2}$$