# Properties

 Label 322.2.m Level $322$ Weight $2$ Character orbit 322.m Rep. character $\chi_{322}(9,\cdot)$ Character field $\Q(\zeta_{33})$ Dimension $320$ 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.m (of order $$33$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q(\zeta_{33})$$ 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 1040 320 720
Cusp forms 880 320 560
Eisenstein series 160 0 160

## Trace form

 $$320 q + 16 q^{4} + 8 q^{6} + 4 q^{7} + 12 q^{9} + O(q^{10})$$ $$320 q + 16 q^{4} + 8 q^{6} + 4 q^{7} + 12 q^{9} + 4 q^{10} - 8 q^{11} - 4 q^{14} - 16 q^{15} + 16 q^{16} + 16 q^{17} - 44 q^{18} - 44 q^{20} + 112 q^{21} - 16 q^{22} - 44 q^{23} - 4 q^{24} - 16 q^{25} - 12 q^{26} - 108 q^{27} + 36 q^{28} - 32 q^{30} - 4 q^{31} + 24 q^{33} - 10 q^{35} - 24 q^{36} - 44 q^{37} + 4 q^{38} - 4 q^{39} + 4 q^{40} + 24 q^{41} + 4 q^{42} + 112 q^{43} - 8 q^{44} - 144 q^{45} - 16 q^{47} - 86 q^{49} - 48 q^{51} + 16 q^{53} - 60 q^{54} - 40 q^{55} - 26 q^{56} + 64 q^{57} + 44 q^{58} - 68 q^{59} + 8 q^{60} - 148 q^{61} + 24 q^{62} - 138 q^{63} - 32 q^{64} + 126 q^{65} + 32 q^{66} - 8 q^{67} - 72 q^{68} + 16 q^{69} - 68 q^{70} + 44 q^{72} - 40 q^{73} - 16 q^{74} - 284 q^{75} - 118 q^{77} - 16 q^{78} + 80 q^{79} - 44 q^{81} - 88 q^{82} - 40 q^{83} - 18 q^{84} + 44 q^{85} + 6 q^{86} + 66 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{90} + 60 q^{91} - 48 q^{93} - 4 q^{94} - 34 q^{95} - 4 q^{96} - 72 q^{97} - 68 q^{98} - 208 q^{99} + O(q^{100})$$

## 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.m.a $160$ $2.571$ None $$-8$$ $$2$$ $$-2$$ $$15$$
322.2.m.b $160$ $2.571$ None $$8$$ $$-2$$ $$2$$ $$-11$$

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

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