# Properties

 Label 147.4.e Level $147$ Weight $4$ Character orbit 147.e Rep. character $\chi_{147}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $40$ Newform subspaces $14$ Sturm bound $74$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$74$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(147, [\chi])$$.

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

## Trace form

 $$40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} + O(q^{10})$$ $$40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} - 46q^{10} + 40q^{11} - 72q^{12} + 4q^{13} + 84q^{15} - 164q^{16} + 132q^{17} - 36q^{18} - 218q^{19} - 872q^{20} - 180q^{22} + 208q^{23} - 54q^{24} - 686q^{25} + 466q^{26} + 108q^{27} + 920q^{29} + 216q^{30} - 348q^{31} + 1050q^{32} - 150q^{33} + 552q^{34} + 1080q^{36} + 550q^{37} - 350q^{38} + 42q^{39} - 42q^{40} - 1208q^{41} - 2076q^{43} - 1112q^{44} + 72q^{45} - 1076q^{46} - 240q^{47} + 1872q^{48} - 920q^{50} + 48q^{51} + 260q^{52} + 2884q^{53} - 108q^{54} + 1972q^{55} - 1140q^{57} + 418q^{58} + 1128q^{59} - 1938q^{60} - 188q^{61} - 3636q^{62} + 2664q^{64} - 336q^{65} + 156q^{66} - 2290q^{67} + 2028q^{68} + 1800q^{69} + 376q^{71} + 702q^{72} + 1350q^{73} + 1534q^{74} - 738q^{75} + 4712q^{76} - 108q^{78} + 248q^{79} + 388q^{80} - 1620q^{81} - 956q^{82} - 1992q^{83} + 2264q^{85} + 4670q^{86} - 1050q^{87} + 6198q^{88} + 2672q^{89} + 828q^{90} - 10360q^{92} - 3006q^{93} - 3204q^{94} - 928q^{95} - 1914q^{96} - 1044q^{97} - 720q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(147, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
147.4.e.a $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$-3$$ $$-18$$ $$0$$ $$q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots$$
147.4.e.b $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$-3$$ $$-4$$ $$0$$ $$q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots$$
147.4.e.c $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$3$$ $$4$$ $$0$$ $$q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots$$
147.4.e.d $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$3$$ $$18$$ $$0$$ $$q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots$$
147.4.e.e $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$12$$ $$0$$ $$q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$$
147.4.e.f $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-12$$ $$0$$ $$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$$
147.4.e.g $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$-3$$ $$-18$$ $$0$$ $$q+3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
147.4.e.h $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$3$$ $$-3$$ $$0$$ $$q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
147.4.e.i $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$3$$ $$18$$ $$0$$ $$q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
147.4.e.j $$4$$ $$8.673$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$-6$$ $$20$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$$
147.4.e.k $$4$$ $$8.673$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$6$$ $$-20$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}-3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$$
147.4.e.l $$4$$ $$8.673$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$3$$ $$-6$$ $$-6$$ $$0$$ $$q+(1+\beta _{1}+\beta _{3})q^{2}+3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots$$
147.4.e.m $$4$$ $$8.673$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$3$$ $$6$$ $$6$$ $$0$$ $$q+(1+\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots$$
147.4.e.n $$6$$ $$8.673$$ 6.0.9924270768.1 None $$-1$$ $$-9$$ $$11$$ $$0$$ $$q-\beta _{1}q^{2}+(-3+3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(147, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(147, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 2}$$