# Properties

 Label 210.2.t Level $210$ Weight $2$ Character orbit 210.t Rep. character $\chi_{210}(59,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $6$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 210.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$23$$

## Dimensions

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

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

## Trace form

 $$32q - 16q^{4} + 6q^{9} + O(q^{10})$$ $$32q - 16q^{4} + 6q^{9} - 6q^{10} + 20q^{15} - 16q^{16} - 24q^{19} + 10q^{21} - 6q^{24} + 6q^{25} - 10q^{30} - 12q^{31} - 12q^{36} - 12q^{39} + 6q^{40} + 6q^{45} - 4q^{46} + 40q^{49} - 4q^{51} - 10q^{60} - 60q^{61} + 32q^{64} + 48q^{66} - 10q^{70} - 96q^{75} - 52q^{79} + 22q^{81} + 16q^{84} - 88q^{85} + 16q^{91} + 96q^{94} + 6q^{96} + 32q^{99} + O(q^{100})$$

## 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.t.a $$4$$ $$1.677$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-2$$ $$-2$$ $$-6$$ $$-10$$ $$q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
210.2.t.b $$4$$ $$1.677$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-2$$ $$-1$$ $$-3$$ $$10$$ $$q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$$
210.2.t.c $$4$$ $$1.677$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$1$$ $$6$$ $$-10$$ $$q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
210.2.t.d $$4$$ $$1.677$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$2$$ $$3$$ $$10$$ $$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
210.2.t.e $$8$$ $$1.677$$ 8.0.3317760000.3 None $$-4$$ $$0$$ $$12$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$
210.2.t.f $$8$$ $$1.677$$ 8.0.3317760000.3 None $$4$$ $$0$$ $$-12$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$

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

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