# Properties

 Label 170.2.b Level $170$ Weight $2$ Character orbit 170.b Rep. character $\chi_{170}(101,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $54$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$170 = 2 \cdot 5 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 170.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$54$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(170, [\chi])$$.

Total New Old
Modular forms 30 6 24
Cusp forms 22 6 16
Eisenstein series 8 0 8

## Trace form

 $$6q + 2q^{2} + 6q^{4} + 2q^{8} - 2q^{9} + O(q^{10})$$ $$6q + 2q^{2} + 6q^{4} + 2q^{8} - 2q^{9} - 12q^{13} - 8q^{15} + 6q^{16} - 2q^{17} - 10q^{18} + 4q^{19} + 24q^{21} - 6q^{25} + 8q^{26} - 4q^{30} + 2q^{32} - 24q^{33} - 18q^{34} + 4q^{35} - 2q^{36} - 8q^{38} + 24q^{42} - 40q^{43} + 32q^{47} + 2q^{49} - 2q^{50} + 4q^{51} - 12q^{52} - 4q^{53} - 8q^{55} - 20q^{59} - 8q^{60} + 6q^{64} - 8q^{67} - 2q^{68} + 32q^{69} + 4q^{70} - 10q^{72} + 4q^{76} + 32q^{77} + 38q^{81} + 16q^{83} + 24q^{84} + 8q^{85} - 24q^{86} - 16q^{87} + 56q^{93} + 4q^{94} - 26q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(170, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
170.2.b.a $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}-q^{8}+\cdots$$
170.2.b.b $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+3iq^{3}+q^{4}+iq^{5}+3iq^{6}+\cdots$$
170.2.b.c $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+iq^{5}+2iq^{7}+q^{8}+3q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(170, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(170, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(85, [\chi])$$$$^{\oplus 2}$$