# Properties

 Label 147.2.g Level $147$ Weight $2$ Character orbit 147.g Rep. character $\chi_{147}(68,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $18$ Newform subspaces $2$ Sturm bound $37$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 147.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$37$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(147, [\chi])$$.

Total New Old
Modular forms 54 34 20
Cusp forms 22 18 4
Eisenstein series 32 16 16

## Trace form

 $$18 q + 3 q^{3} + 6 q^{4} - 5 q^{9} + O(q^{10})$$ $$18 q + 3 q^{3} + 6 q^{4} - 5 q^{9} - 6 q^{12} - 16 q^{15} + 20 q^{16} - 16 q^{18} + 9 q^{19} - 32 q^{22} + 13 q^{25} - 24 q^{30} - 15 q^{31} + 4 q^{36} - 17 q^{37} - 5 q^{39} + 22 q^{43} - 32 q^{46} + 24 q^{51} + 6 q^{52} - 46 q^{57} + 24 q^{60} - 12 q^{61} + 32 q^{64} + 37 q^{67} + 32 q^{72} + 27 q^{73} + 15 q^{75} + 80 q^{78} - 3 q^{79} + 15 q^{81} - 32 q^{85} - 32 q^{88} + q^{93} + 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(147, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.2.g.a $2$ $1.174$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{9}+\cdots$$
147.2.g.b $16$ $1.174$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{13}q^{2}+(\beta _{7}-\beta _{9})q^{3}+(1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(147, [\chi])$$ into lower level spaces

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