# Properties

 Label 147.6.c Level $147$ Weight $6$ Character orbit 147.c Rep. character $\chi_{147}(146,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $4$ Sturm bound $112$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 147.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$112$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(147, [\chi])$$.

Total New Old
Modular forms 102 70 32
Cusp forms 86 62 24
Eisenstein series 16 8 8

## Trace form

 $$62 q - 892 q^{4} + 602 q^{9} + O(q^{10})$$ $$62 q - 892 q^{4} + 602 q^{9} - 2192 q^{15} + 7796 q^{16} + 2860 q^{18} + 14012 q^{22} + 24714 q^{25} + 40500 q^{30} - 69700 q^{36} - 16394 q^{37} + 12026 q^{39} + 68710 q^{43} - 65680 q^{46} - 1272 q^{51} - 136550 q^{57} + 38668 q^{58} + 216420 q^{60} + 122156 q^{64} - 53578 q^{67} - 81104 q^{72} - 330416 q^{78} + 171262 q^{79} + 437682 q^{81} + 347128 q^{85} - 1013340 q^{88} - 248194 q^{93} - 398784 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(147, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.6.c.a $2$ $23.576$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+9\zeta_{6}q^{3}+2^{5}q^{4}-3^{5}q^{9}+288\zeta_{6}q^{12}+\cdots$$
147.6.c.b $4$ $23.576$ $$\Q(\sqrt{-3}, \sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{1}q^{2}+(-8\beta _{2}-\beta _{3})q^{3}-6^{2}q^{4}+\cdots$$
147.6.c.c $16$ $23.576$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+\beta _{5}q^{3}+(-11-\beta _{2})q^{4}+\cdots$$
147.6.c.d $40$ $23.576$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{6}^{\mathrm{old}}(147, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(147, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$