# Properties

 Label 210.2.i Level $210$ Weight $2$ Character orbit 210.i Rep. character $\chi_{210}(121,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $4$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 112 8 104
Cusp forms 80 8 72
Eisenstein series 32 0 32

## Trace form

 $$8 q - 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{4} - 4 q^{9} - 4 q^{10} + 4 q^{11} + 16 q^{13} - 12 q^{14} - 4 q^{16} + 8 q^{17} + 4 q^{19} - 16 q^{22} - 4 q^{25} + 4 q^{26} - 32 q^{29} + 8 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{35} + 8 q^{36} - 8 q^{37} + 8 q^{38} - 16 q^{39} - 4 q^{40} + 24 q^{41} + 16 q^{42} + 48 q^{43} + 4 q^{44} - 4 q^{46} + 16 q^{47} + 8 q^{49} - 8 q^{52} + 24 q^{53} - 16 q^{55} + 32 q^{57} - 32 q^{59} - 8 q^{61} + 32 q^{62} + 8 q^{64} + 4 q^{65} - 8 q^{67} + 8 q^{68} - 32 q^{69} - 48 q^{71} + 8 q^{73} + 12 q^{74} - 8 q^{76} - 24 q^{77} + 16 q^{78} + 8 q^{79} - 4 q^{81} - 16 q^{82} + 16 q^{83} - 16 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{89} + 8 q^{90} + 32 q^{91} + 12 q^{94} + 8 q^{95} - 64 q^{97} - 8 q^{99} + O(q^{100})$$

## 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.i.a $2$ $1.677$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$-1$$ $$4$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
210.2.i.b $2$ $1.677$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-1$$ $$-4$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
210.2.i.c $2$ $1.677$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$1$$ $$-4$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
210.2.i.d $2$ $1.677$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$4$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$

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

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