# Properties

 Label 140.2.q Level $140$ Weight $2$ Character orbit 140.q Rep. character $\chi_{140}(9,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $2$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

## Trace form

 $$8 q - q^{5} + O(q^{10})$$ $$8 q - q^{5} + 6 q^{11} - 6 q^{15} - 2 q^{19} - 9 q^{25} - 4 q^{29} + 2 q^{31} + 5 q^{35} - 12 q^{39} - 60 q^{41} + 10 q^{49} - 18 q^{51} + 54 q^{55} + 2 q^{59} + 24 q^{61} + 16 q^{65} + 48 q^{69} + 24 q^{71} - 27 q^{75} + 14 q^{79} + 36 q^{81} - 10 q^{85} - 28 q^{89} + 20 q^{91} - 29 q^{95} + O(q^{100})$$

## 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.q.a $4$ $1.118$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$-6$$ $$1$$ $$-3$$ $$q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots$$
140.2.q.b $4$ $1.118$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$6$$ $$-2$$ $$3$$ $$q+(2-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots$$

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

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