Properties

 Label 210.2.b Level $210$ Weight $2$ Character orbit 210.b Rep. character $\chi_{210}(41,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$17$$

Dimensions

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

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

 $$8q - 8q^{4} + 12q^{7} + O(q^{10})$$ $$8q - 8q^{4} + 12q^{7} - 4q^{15} + 8q^{16} - 16q^{18} - 16q^{21} + 8q^{25} - 12q^{28} - 4q^{30} + 24q^{37} - 24q^{39} - 4q^{42} + 32q^{43} + 32q^{46} - 32q^{51} + 24q^{57} + 8q^{58} + 4q^{60} + 20q^{63} - 8q^{64} - 96q^{67} - 12q^{70} + 16q^{72} - 16q^{78} + 8q^{81} + 16q^{84} + 24q^{85} - 32q^{91} + 40q^{93} + O(q^{100})$$

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.b.a $$4$$ $$1.677$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-2$$ $$4$$ $$6$$ $$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+q^{5}+\cdots$$
210.2.b.b $$4$$ $$1.677$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$2$$ $$-4$$ $$6$$ $$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}-q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$