# Properties

 Label 210.3.c Level 210 Weight 3 Character orbit c Rep. character $$\chi_{210}(29,\cdot)$$ Character field $$\Q$$ Dimension 24 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ 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 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

## Trace form

 $$24q + 48q^{4} + 44q^{9} + O(q^{10})$$ $$24q + 48q^{4} + 44q^{9} + 16q^{10} + 4q^{15} + 96q^{16} - 80q^{19} - 28q^{21} + 48q^{25} - 56q^{30} + 224q^{31} + 128q^{34} + 88q^{36} - 92q^{39} + 32q^{40} - 72q^{45} - 144q^{46} - 168q^{49} - 284q^{51} - 144q^{54} - 320q^{55} + 8q^{60} + 192q^{64} + 224q^{66} - 152q^{69} - 56q^{70} + 48q^{75} - 160q^{76} - 72q^{79} - 212q^{81} - 56q^{84} - 64q^{85} - 240q^{90} + 168q^{91} - 128q^{94} - 876q^{99} + O(q^{100})$$

## 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.c.a $$24$$ $$5.722$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{3}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database