Properties

 Label 147.4.g Level $147$ Weight $4$ Character orbit 147.g Rep. character $\chi_{147}(68,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $5$ Sturm bound $74$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 147.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$74$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$19$$

Dimensions

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

Total New Old
Modular forms 128 88 40
Cusp forms 96 72 24
Eisenstein series 32 16 16

Trace form

 $$72 q + 3 q^{3} + 130 q^{4} + 19 q^{9} + O(q^{10})$$ $$72 q + 3 q^{3} + 130 q^{4} + 19 q^{9} - 30 q^{10} + 192 q^{12} + 110 q^{15} - 638 q^{16} - 106 q^{18} - 300 q^{19} + 52 q^{22} - 414 q^{24} - 444 q^{25} + 1086 q^{30} + 930 q^{31} + 855 q^{33} - 572 q^{36} - 368 q^{37} + 1018 q^{39} - 2298 q^{40} + 172 q^{43} - 2367 q^{45} - 1640 q^{46} + 2043 q^{51} + 3000 q^{52} + 4158 q^{54} + 734 q^{57} - 4466 q^{58} + 3078 q^{60} - 2358 q^{61} - 460 q^{64} - 2934 q^{66} - 984 q^{67} + 4964 q^{72} + 2904 q^{73} + 2418 q^{75} - 592 q^{78} - 1110 q^{79} - 345 q^{81} - 5040 q^{82} - 2244 q^{85} - 1638 q^{87} + 614 q^{88} + 2125 q^{93} + 1356 q^{94} + 4410 q^{96} - 3978 q^{99} + O(q^{100})$$

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.g.a $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-9$$ $$0$$ $$0$$ $$q+(-3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots$$
147.4.g.b $$2$$ $$8.673$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$9$$ $$0$$ $$0$$ $$q+(3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+3^{3}\zeta_{6}q^{9}+\cdots$$
147.4.g.c $$8$$ $$8.673$$ 8.0.$$\cdots$$.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{3}+(9-9\beta _{1}+\cdots)q^{4}+\cdots$$
147.4.g.d $$12$$ $$8.673$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(\beta _{2}-\beta _{6})q^{2}+(-\beta _{7}-\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots$$
147.4.g.e $$48$$ $$8.673$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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