# Properties

 Label 322.2.k Level $322$ Weight $2$ Character orbit 322.k Rep. character $\chi_{322}(83,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $160$ Newform subspaces $2$ Sturm bound $96$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$322 = 2 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 322.k (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(322, [\chi])$$.

Total New Old
Modular forms 520 160 360
Cusp forms 440 160 280
Eisenstein series 80 0 80

## Trace form

 $$160q - 16q^{4} + 8q^{9} + O(q^{10})$$ $$160q - 16q^{4} + 8q^{9} - 16q^{16} - 20q^{18} - 66q^{21} + 36q^{23} - 52q^{25} - 22q^{28} + 24q^{29} + 44q^{30} + 14q^{35} + 8q^{36} - 44q^{37} - 16q^{39} - 44q^{43} + 50q^{49} + 24q^{50} - 44q^{51} + 22q^{56} - 44q^{57} - 80q^{58} + 110q^{63} - 16q^{64} - 308q^{65} + 80q^{70} - 16q^{71} - 64q^{72} + 126q^{77} - 176q^{79} + 36q^{81} + 22q^{84} + 60q^{85} - 44q^{86} - 8q^{92} + 104q^{93} + 64q^{95} - 60q^{98} + 88q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(322, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
322.2.k.a $$80$$ $$2.571$$ None $$-8$$ $$0$$ $$0$$ $$-11$$
322.2.k.b $$80$$ $$2.571$$ None $$8$$ $$0$$ $$0$$ $$11$$

## Decomposition of $$S_{2}^{\mathrm{old}}(322, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(322, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 2}$$