# Properties

 Label 140.2.k Level $140$ Weight $2$ Character orbit 140.k Rep. character $\chi_{140}(43,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $36$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 56 36 20
Cusp forms 40 36 4
Eisenstein series 16 0 16

## Trace form

 $$36 q - 8 q^{6} + O(q^{10})$$ $$36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97} + O(q^{100})$$

## 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.k.a $36$ $1.118$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 2}$$