# Properties

 Label 1323.2.s Level $1323$ Weight $2$ Character orbit 1323.s Rep. character $\chi_{1323}(656,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $4$ Sturm bound $336$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$336$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1323, [\chi])$$.

Total New Old
Modular forms 384 88 296
Cusp forms 288 72 216
Eisenstein series 96 16 80

## Trace form

 $$72q - 3q^{2} + 31q^{4} - 6q^{5} + O(q^{10})$$ $$72q - 3q^{2} + 31q^{4} - 6q^{5} + 6q^{10} - 3q^{13} - 23q^{16} - 9q^{17} + 6q^{19} - 6q^{20} - 8q^{22} + 42q^{25} + 6q^{26} - 6q^{29} + 15q^{31} + 69q^{32} + 6q^{34} + q^{37} + 54q^{38} - 6q^{41} - 8q^{43} - 69q^{44} + 16q^{46} + 15q^{47} - 3q^{50} - 36q^{53} - 2q^{58} - 18q^{59} - 36q^{61} + 24q^{62} - 28q^{64} + 36q^{65} + 6q^{67} - 48q^{68} + 6q^{73} - 18q^{79} - 45q^{80} - 30q^{83} - 21q^{85} - 46q^{88} + 27q^{89} + 84q^{92} + 3q^{94} + 141q^{95} - 3q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1323, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1323.2.s.a $$2$$ $$10.564$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$0$$ $$-6$$ $$0$$ $$q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-3q^{5}+(1-2\zeta_{6})q^{8}+\cdots$$
1323.2.s.b $$10$$ $$10.564$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots$$
1323.2.s.c $$12$$ $$10.564$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$$
1323.2.s.d $$48$$ $$10.564$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1323, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1323, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$