# Properties

 Label 210.3.p Level 210 Weight 3 Character orbit p Rep. character $$\chi_{210}(19,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 32 Newform subspaces 1 Sturm bound 144 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 210.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(210, [\chi])$$.

Total New Old
Modular forms 208 32 176
Cusp forms 176 32 144
Eisenstein series 32 0 32

## Trace form

 $$32q + 32q^{4} + 12q^{5} - 48q^{9} + O(q^{10})$$ $$32q + 32q^{4} + 12q^{5} - 48q^{9} - 24q^{10} + 48q^{11} - 16q^{14} + 24q^{15} - 64q^{16} + 48q^{19} - 24q^{21} + 72q^{25} + 96q^{26} + 176q^{29} - 24q^{30} - 48q^{31} + 68q^{35} - 192q^{36} - 72q^{39} - 48q^{40} - 96q^{44} - 36q^{45} + 32q^{46} - 272q^{49} + 192q^{50} - 24q^{51} - 64q^{56} + 744q^{59} + 24q^{60} - 672q^{61} - 256q^{64} + 172q^{65} + 320q^{70} - 144q^{71} - 416q^{74} - 144q^{75} + 128q^{79} - 48q^{80} - 144q^{81} - 96q^{84} - 736q^{85} + 304q^{86} - 48q^{89} + 976q^{91} + 528q^{94} + 236q^{95} - 288q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(210, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
210.3.p.a $$32$$ $$5.722$$ None $$0$$ $$0$$ $$12$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(210, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database