# Properties

 Label 220.2.b Level $220$ Weight $2$ Character orbit 220.b Rep. character $\chi_{220}(89,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$220 = 2^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 220.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(220, [\chi])$$.

Total New Old
Modular forms 42 6 36
Cusp forms 30 6 24
Eisenstein series 12 0 12

## Trace form

 $$6 q - q^{5} - 4 q^{9} + O(q^{10})$$ $$6 q - q^{5} - 4 q^{9} + 2 q^{11} + 11 q^{15} - 8 q^{19} - 12 q^{21} + 3 q^{25} + 16 q^{29} + 6 q^{31} - 2 q^{35} - 32 q^{39} + 20 q^{45} - 14 q^{49} + 12 q^{51} + 3 q^{55} - 42 q^{59} - 8 q^{65} - 2 q^{69} - 2 q^{71} - 23 q^{75} + 44 q^{79} + 34 q^{81} + 2 q^{85} - 22 q^{89} - 12 q^{95} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(220, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
220.2.b.a $2$ $1.757$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}+iq^{7}+3q^{9}-q^{11}+\cdots$$
220.2.b.b $4$ $1.757$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(220, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(220, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 2}$$