# Properties

 Label 1323.2.o Level $1323$ Weight $2$ Character orbit 1323.o Rep. character $\chi_{1323}(440,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $5$ Sturm bound $336$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$336$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## 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

 $$72q - 6q^{2} + 34q^{4} + O(q^{10})$$ $$72q - 6q^{2} + 34q^{4} + 6q^{11} - 26q^{16} + 4q^{22} + 36q^{23} - 18q^{25} + 48q^{29} - 42q^{32} + 4q^{37} + 4q^{43} + 16q^{46} - 30q^{50} - 2q^{58} - 40q^{64} - 108q^{65} - 12q^{67} + 66q^{74} - 6q^{85} + 90q^{86} - 22q^{88} + 84q^{92} - 42q^{95} + O(q^{100})$$

## 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.o.a $$2$$ $$10.564$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$0$$ $$-3$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$$
1323.2.o.b $$2$$ $$10.564$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$0$$ $$3$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$$
1323.2.o.c $$10$$ $$10.564$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$$
1323.2.o.d $$10$$ $$10.564$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$$
1323.2.o.e $$48$$ $$10.564$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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