# Properties

 Label 126.2.g Level $126$ Weight $2$ Character orbit 126.g Rep. character $\chi_{126}(37,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $4$ Sturm bound $48$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 126.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(126, [\chi])$$.

Total New Old
Modular forms 64 8 56
Cusp forms 32 8 24
Eisenstein series 32 0 32

## Trace form

 $$8 q - 4 q^{4} + 4 q^{5} + 4 q^{7} + O(q^{10})$$ $$8 q - 4 q^{4} + 4 q^{5} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 8 q^{14} - 4 q^{16} - 4 q^{17} - 8 q^{19} - 8 q^{20} - 8 q^{22} - 4 q^{23} - 8 q^{25} + 4 q^{26} + 4 q^{28} - 8 q^{29} + 12 q^{31} + 16 q^{34} + 8 q^{35} + 16 q^{37} + 12 q^{38} - 4 q^{40} - 32 q^{43} + 8 q^{44} + 16 q^{46} - 12 q^{47} - 28 q^{49} + 16 q^{50} - 12 q^{53} - 8 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} + 8 q^{64} - 12 q^{65} + 8 q^{67} - 4 q^{68} + 28 q^{70} + 8 q^{71} - 16 q^{73} - 12 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} + 64 q^{85} + 12 q^{86} + 4 q^{88} - 24 q^{91} + 8 q^{92} - 24 q^{94} - 4 q^{95} - 40 q^{97} - 24 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(126, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.2.g.a $2$ $1.006$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-3$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$$
126.2.g.b $2$ $1.006$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$3$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots$$
126.2.g.c $2$ $1.006$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$$
126.2.g.d $2$ $1.006$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$3$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(126, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(126, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$