# Properties

 Label 210.2.n Level $210$ Weight $2$ Character orbit 210.n Rep. character $\chi_{210}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 210.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(210, [\chi])$$.

Total New Old
Modular forms 112 16 96
Cusp forms 80 16 64
Eisenstein series 32 0 32

## Trace form

 $$16q + 8q^{4} - 4q^{5} + 8q^{6} + 8q^{9} + O(q^{10})$$ $$16q + 8q^{4} - 4q^{5} + 8q^{6} + 8q^{9} - 2q^{10} + 4q^{11} - 4q^{14} + 4q^{15} - 8q^{16} + 20q^{19} - 8q^{20} + 8q^{21} + 4q^{24} - 6q^{25} - 4q^{26} - 48q^{29} + 4q^{30} + 12q^{31} - 32q^{34} - 20q^{35} + 16q^{36} + 8q^{39} + 2q^{40} - 72q^{41} - 4q^{44} + 4q^{45} - 12q^{46} + 20q^{49} + 16q^{50} - 8q^{51} + 4q^{54} + 20q^{55} - 8q^{56} - 16q^{59} + 2q^{60} - 8q^{61} - 16q^{64} - 32q^{65} - 16q^{66} - 48q^{69} - 26q^{70} + 64q^{71} + 28q^{74} - 8q^{75} + 40q^{76} + 20q^{79} - 4q^{80} - 8q^{81} + 16q^{84} + 8q^{85} + 32q^{86} + 8q^{89} - 4q^{90} + 8q^{91} + 20q^{94} + 28q^{95} - 4q^{96} + 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(210, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
210.2.n.a $$4$$ $$1.677$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
210.2.n.b $$12$$ $$1.677$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{8})q^{3}+(1+\beta _{10})q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(210, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$