# Properties

 Label 322.2.i Level $322$ Weight $2$ Character orbit 322.i Rep. character $\chi_{322}(29,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $120$ Newform subspaces $5$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$322 = 2 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 322.i (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 520 120 400
Cusp forms 440 120 320
Eisenstein series 80 0 80

## Trace form

 $$120 q + 8 q^{3} - 12 q^{4} + 8 q^{5} - 4 q^{9} + O(q^{10})$$ $$120 q + 8 q^{3} - 12 q^{4} + 8 q^{5} - 4 q^{9} + 12 q^{11} + 8 q^{12} + 24 q^{13} + 4 q^{14} - 4 q^{15} - 12 q^{16} - 28 q^{17} - 36 q^{18} - 20 q^{19} + 8 q^{20} + 4 q^{21} - 32 q^{22} - 20 q^{23} - 36 q^{26} + 56 q^{27} - 4 q^{29} - 20 q^{30} + 12 q^{31} + 4 q^{33} + 16 q^{34} + 8 q^{35} - 4 q^{36} + 16 q^{38} - 8 q^{39} + 4 q^{41} + 4 q^{42} - 8 q^{43} + 12 q^{44} + 72 q^{45} + 20 q^{46} - 24 q^{47} + 8 q^{48} - 12 q^{49} + 16 q^{50} + 20 q^{51} + 24 q^{52} + 16 q^{53} + 24 q^{54} - 96 q^{55} + 4 q^{56} - 88 q^{57} + 32 q^{58} - 104 q^{59} - 4 q^{60} + 32 q^{61} - 92 q^{62} + 24 q^{63} - 12 q^{64} + 48 q^{65} - 112 q^{66} - 12 q^{67} + 16 q^{68} - 124 q^{69} + 8 q^{70} - 124 q^{71} + 8 q^{72} - 8 q^{73} - 124 q^{74} + 84 q^{75} + 24 q^{76} - 52 q^{78} + 52 q^{79} - 36 q^{80} - 80 q^{81} + 24 q^{82} - 96 q^{83} + 4 q^{84} - 24 q^{85} + 36 q^{86} + 72 q^{87} + 12 q^{88} + 52 q^{89} + 112 q^{90} - 32 q^{91} + 24 q^{92} + 88 q^{93} + 16 q^{94} + 84 q^{95} - 64 q^{97} + 156 q^{99} + O(q^{100})$$

## 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.i.a $10$ $2.571$ $$\Q(\zeta_{22})$$ None $$1$$ $$-3$$ $$5$$ $$1$$ $$q-\zeta_{22}^{4}q^{2}+(-1-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$$
322.2.i.b $10$ $2.571$ $$\Q(\zeta_{22})$$ None $$1$$ $$5$$ $$8$$ $$1$$ $$q-\zeta_{22}^{4}q^{2}+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots$$
322.2.i.c $20$ $2.571$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-2$$ $$4$$ $$-5$$ $$-2$$ $$q+\beta _{19}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$$
322.2.i.d $40$ $2.571$ None $$-4$$ $$0$$ $$9$$ $$4$$
322.2.i.e $40$ $2.571$ None $$4$$ $$2$$ $$-9$$ $$-4$$

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

$$S_{2}^{\mathrm{old}}(322, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(46, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 2}$$