# Properties

 Label 170.2.c Level $170$ Weight $2$ Character orbit 170.c Rep. character $\chi_{170}(69,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $54$ Trace bound $1$

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## Defining parameters

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

 $$8q - 8q^{4} + 4q^{5} - 12q^{9} + O(q^{10})$$ $$8q - 8q^{4} + 4q^{5} - 12q^{9} - 4q^{10} + 8q^{15} + 8q^{16} + 12q^{19} - 4q^{20} - 24q^{21} + 4q^{25} - 4q^{26} - 24q^{29} + 20q^{30} + 16q^{31} - 4q^{34} + 20q^{35} + 12q^{36} - 40q^{39} + 4q^{40} + 32q^{41} + 12q^{45} - 8q^{46} + 16q^{49} - 12q^{50} + 4q^{51} - 24q^{54} - 8q^{55} - 28q^{59} - 8q^{60} - 24q^{61} - 8q^{64} + 16q^{66} + 48q^{69} + 4q^{70} - 32q^{71} + 8q^{75} - 12q^{76} - 24q^{79} + 4q^{80} + 40q^{81} + 24q^{84} + 4q^{85} + 16q^{86} + 20q^{89} + 20q^{90} - 24q^{91} + 36q^{94} - 56q^{99} + O(q^{100})$$

## 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.c.a $$2$$ $$1.357$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots$$
170.2.c.b $$6$$ $$1.357$$ 6.0.5161984.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}-q^{4}+\cdots$$

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

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