# Properties

 Label 170.2.d Level 170 Weight 2 Character orbit d Rep. character $$\chi_{170}(169,\cdot)$$ Character field $$\Q$$ Dimension 8 Newform subspaces 3 Sturm bound 54 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$170 = 2 \cdot 5 \cdot 17$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 170.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$85$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$54$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

## Trace form

 $$8q - 8q^{4} + 12q^{9} + O(q^{10})$$ $$8q - 8q^{4} + 12q^{9} + 16q^{15} + 8q^{16} - 12q^{19} - 40q^{21} - 4q^{25} + 20q^{26} - 20q^{30} - 4q^{34} + 4q^{35} - 12q^{36} + 32q^{49} + 4q^{50} + 36q^{51} - 68q^{59} - 16q^{60} - 8q^{64} - 32q^{69} + 44q^{70} + 12q^{76} + 8q^{81} + 40q^{84} + 16q^{85} - 48q^{86} + 68q^{89} + 28q^{94} + O(q^{100})$$

## 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.d.a $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$-4$$ $$q+iq^{2}-q^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots$$
170.2.d.b $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$4$$ $$q+iq^{2}+q^{3}-q^{4}+(2-i)q^{5}+iq^{6}+\cdots$$
170.2.d.c $$4$$ $$1.357$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots$$

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

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