# Properties

 Label 252.9.d Level $252$ Weight $9$ Character orbit 252.d Rep. character $\chi_{252}(181,\cdot)$ Character field $\Q$ Dimension $26$ Newform subspaces $4$ Sturm bound $432$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 252.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$432$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(252, [\chi])$$.

Total New Old
Modular forms 396 26 370
Cusp forms 372 26 346
Eisenstein series 24 0 24

## Trace form

 $$26 q + 1870 q^{7} + O(q^{10})$$ $$26 q + 1870 q^{7} + 13104 q^{11} + 33984 q^{23} - 2355862 q^{25} - 955440 q^{29} + 2795400 q^{35} - 798724 q^{37} + 4749788 q^{43} - 12584902 q^{49} + 8469792 q^{53} + 22705776 q^{65} + 12334564 q^{67} + 35103312 q^{71} + 12620304 q^{77} + 20380804 q^{79} - 4798896 q^{85} + 29955600 q^{91} - 189214992 q^{95} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.9.d.a $$2$$ $$102.659$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-4034$$ $$q+(-2017-47\zeta_{6})q^{7}-1606\zeta_{6}q^{13}+\cdots$$
252.9.d.b $$6$$ $$102.659$$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$2166$$ $$q-\beta _{1}q^{5}+(19^{2}-\beta _{3})q^{7}+(-4082+\cdots)q^{11}+\cdots$$
252.9.d.c $$8$$ $$102.659$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$6076$$ $$q-\beta _{1}q^{5}+(756-7\beta _{2})q^{7}-\beta _{5}q^{11}+\cdots$$
252.9.d.d $$10$$ $$102.659$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-2338$$ $$q+(\beta _{1}+\beta _{6})q^{5}+(-234-2\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$