# Properties

 Label 140.2.e Level $140$ Weight $2$ Character orbit 140.e Rep. character $\chi_{140}(29,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $48$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(140, [\chi])$$.

Total New Old
Modular forms 30 4 26
Cusp forms 18 4 14
Eisenstein series 12 0 12

## Trace form

 $$4 q - 2 q^{5} - 6 q^{9} + O(q^{10})$$ $$4 q - 2 q^{5} - 6 q^{9} + 6 q^{11} - 6 q^{15} + 8 q^{19} + 6 q^{21} - 2 q^{29} - 20 q^{31} - 2 q^{35} - 6 q^{39} + 30 q^{45} - 4 q^{49} - 30 q^{51} - 12 q^{55} + 28 q^{59} - 12 q^{61} + 14 q^{65} - 12 q^{69} + 24 q^{71} + 24 q^{75} + 22 q^{79} + 36 q^{81} - 26 q^{85} + 4 q^{89} + 10 q^{91} - 40 q^{95} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(140, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.2.e.a $2$ $1.118$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+3iq^{3}+(-2+i)q^{5}-iq^{7}-6q^{9}+\cdots$$
140.2.e.b $2$ $1.118$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+iq^{7}+3q^{9}-4iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(140, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$