# Properties

 Label 32.2.g Level $32$ Weight $2$ Character orbit 32.g Rep. character $\chi_{32}(5,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $12$ Newform subspaces $2$ Sturm bound $8$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 32.g (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$2$$ Sturm bound: $$8$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(32, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + O(q^{10})$$ $$12 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - 4 q^{11} + 12 q^{12} - 4 q^{13} + 12 q^{14} + 16 q^{16} + 16 q^{18} - 4 q^{19} + 12 q^{20} - 4 q^{21} + 8 q^{22} + 4 q^{23} - 16 q^{24} - 4 q^{25} - 24 q^{26} + 20 q^{27} - 24 q^{28} - 4 q^{29} - 36 q^{30} + 16 q^{31} - 24 q^{32} - 8 q^{33} - 16 q^{34} + 20 q^{35} - 32 q^{36} - 4 q^{37} + 4 q^{38} + 20 q^{39} + 8 q^{40} - 4 q^{41} + 16 q^{42} + 4 q^{43} + 36 q^{44} + 8 q^{45} + 28 q^{46} + 48 q^{48} + 36 q^{50} - 8 q^{51} + 4 q^{52} + 12 q^{53} + 8 q^{54} - 36 q^{55} + 8 q^{56} - 4 q^{57} - 8 q^{58} - 36 q^{59} - 8 q^{60} + 28 q^{61} - 24 q^{62} - 48 q^{63} - 40 q^{64} - 8 q^{65} - 28 q^{66} - 44 q^{67} + 16 q^{68} + 28 q^{69} - 16 q^{70} - 36 q^{71} + 20 q^{72} - 4 q^{73} + 12 q^{74} - 16 q^{75} - 4 q^{76} + 12 q^{77} + 36 q^{78} - 8 q^{80} - 4 q^{82} + 36 q^{83} + 16 q^{84} + 16 q^{85} - 24 q^{86} + 52 q^{87} - 4 q^{89} + 8 q^{90} + 44 q^{91} - 40 q^{92} - 16 q^{93} + 8 q^{94} + 56 q^{95} - 8 q^{97} - 24 q^{98} + 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(32, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.2.g.a $4$ $0.256$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$4$$ $$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$$
32.2.g.b $8$ $0.256$ 8.0.18939904.2 None $$-4$$ $$-4$$ $$0$$ $$-8$$ $$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$$