# Properties

 Label 126.9.s Level $126$ Weight $9$ Character orbit 126.s Rep. character $\chi_{126}(53,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $2$ Sturm bound $216$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 126.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$216$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(126, [\chi])$$.

Total New Old
Modular forms 400 40 360
Cusp forms 368 40 328
Eisenstein series 32 0 32

## Trace form

 $$40 q + 2560 q^{4} + 68 q^{7} + O(q^{10})$$ $$40 q + 2560 q^{4} + 68 q^{7} + 11776 q^{10} + 151368 q^{13} - 327680 q^{16} - 87268 q^{19} + 81920 q^{22} + 1153916 q^{25} - 96256 q^{28} - 5100972 q^{31} - 3653632 q^{34} + 3706964 q^{37} - 1507328 q^{40} + 5325704 q^{43} + 6422528 q^{46} - 41835428 q^{49} + 9687552 q^{52} - 18881344 q^{55} + 16440832 q^{58} - 70986672 q^{61} - 83886080 q^{64} + 52674700 q^{67} - 40308736 q^{70} - 148449164 q^{73} - 22340608 q^{76} - 72836820 q^{79} - 133189632 q^{82} + 112996352 q^{85} + 5242880 q^{88} - 511983852 q^{91} + 74222592 q^{94} - 389268176 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(126, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.9.s.a $20$ $51.330$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-3710$$ $$q-8\beta _{3}q^{2}+(2^{7}+2^{7}\beta _{5})q^{4}+(19\beta _{3}+\cdots)q^{5}+\cdots$$
126.9.s.b $20$ $51.330$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$3778$$ $$q-8\beta _{2}q^{2}+(2^{7}+2^{7}\beta _{6})q^{4}+(-93\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(126, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(126, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$