# Properties

 Label 210.3.f Level $210$ Weight $3$ Character orbit 210.f Rep. character $\chi_{210}(181,\cdot)$ Character field $\Q$ Dimension $8$ 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.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ 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 8 96
Cusp forms 88 8 80
Eisenstein series 16 0 16

## Trace form

 $$8 q + 16 q^{4} - 24 q^{9} + O(q^{10})$$ $$8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} + 96 q^{22} - 40 q^{25} - 144 q^{29} - 80 q^{35} - 48 q^{36} - 48 q^{37} - 48 q^{39} - 48 q^{42} - 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} + 128 q^{53} + 64 q^{56} + 144 q^{57} + 224 q^{58} + 64 q^{64} + 80 q^{65} - 192 q^{67} + 176 q^{71} - 160 q^{74} + 192 q^{77} - 96 q^{78} - 288 q^{79} + 72 q^{81} - 240 q^{85} - 64 q^{86} + 192 q^{88} + 64 q^{91} + 336 q^{93} + 80 q^{95} + 48 q^{99} + O(q^{100})$$

## 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.f.a $8$ $5.722$ 8.0.3317760000.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+2q^{4}+\beta _{6}q^{5}+\beta _{3}q^{6}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(210, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$