# Properties

 Label 440.2.b Level $440$ Weight $2$ Character orbit 440.b Rep. character $\chi_{440}(89,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $4$ Sturm bound $144$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$440 = 2^{3} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 440.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(440, [\chi])$$.

Total New Old
Modular forms 80 14 66
Cusp forms 64 14 50
Eisenstein series 16 0 16

## Trace form

 $$14 q + 4 q^{5} - 14 q^{9} + O(q^{10})$$ $$14 q + 4 q^{5} - 14 q^{9} + 6 q^{11} - 14 q^{15} - 8 q^{21} - 8 q^{25} - 4 q^{29} + 4 q^{35} + 16 q^{39} + 20 q^{41} - 14 q^{45} - 18 q^{49} - 24 q^{51} - 20 q^{59} + 52 q^{61} - 32 q^{65} + 12 q^{69} + 8 q^{71} + 50 q^{75} + 40 q^{79} + 46 q^{81} - 20 q^{85} + 20 q^{89} - 40 q^{91} + 24 q^{95} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(440, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.b.a $2$ $3.513$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots$$
440.2.b.b $2$ $3.513$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-i)q^{5}-2iq^{7}-q^{9}+q^{11}+\cdots$$
440.2.b.c $2$ $3.513$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots$$
440.2.b.d $8$ $3.513$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(440, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(440, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 2}$$