# Properties

 Label 161.2.k Level $161$ Weight $2$ Character orbit 161.k Rep. character $\chi_{161}(20,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $140$ Newform subspaces $2$ Sturm bound $32$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$161 = 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 161.k (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(161, [\chi])$$.

Total New Old
Modular forms 180 180 0
Cusp forms 140 140 0
Eisenstein series 40 40 0

## Trace form

 $$140q - 20q^{2} - 28q^{4} - 11q^{7} - 16q^{8} + O(q^{10})$$ $$140q - 20q^{2} - 28q^{4} - 11q^{7} - 16q^{8} - 22q^{11} - 11q^{14} - 22q^{15} - 26q^{16} + 8q^{18} + 22q^{21} - 44q^{23} - 10q^{25} + 33q^{28} - 42q^{29} - 66q^{30} - 6q^{32} - 13q^{35} + 27q^{36} + 22q^{37} - 14q^{39} - 121q^{42} + 22q^{43} + 99q^{44} - 58q^{46} - 55q^{49} + 85q^{50} + 22q^{51} - 22q^{53} - 132q^{56} + 22q^{57} + 81q^{58} - 22q^{60} - 66q^{63} + 48q^{64} + 132q^{65} - 22q^{67} - 54q^{70} - 6q^{71} + 262q^{72} - 33q^{74} - 130q^{77} + 162q^{78} + 66q^{79} - 96q^{81} - 77q^{84} + 110q^{85} + 22q^{86} - 99q^{88} + 244q^{92} - 108q^{93} - 80q^{95} + 7q^{98} + 132q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(161, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
161.2.k.a $$20$$ $$1.286$$ 20.0.$$\cdots$$.2 $$\Q(\sqrt{-7})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{6}-\beta _{14})q^{2}+(-\beta _{2}+\beta _{13}+\cdots)q^{4}+\cdots$$
161.2.k.b $$120$$ $$1.286$$ None $$-22$$ $$0$$ $$0$$ $$-11$$