# Properties

 Label 140.2.g Level $140$ Weight $2$ Character orbit 140.g Rep. character $\chi_{140}(111,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $3$ Sturm bound $48$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$3$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

## Trace form

 $$16 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 16 q^{9} + O(q^{10})$$ $$16 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 16 q^{9} - 14 q^{14} + 2 q^{16} - 30 q^{18} - 12 q^{21} + 32 q^{22} - 16 q^{25} - 2 q^{28} - 8 q^{29} - 2 q^{32} - 30 q^{36} - 32 q^{37} - 4 q^{42} - 36 q^{44} + 28 q^{46} + 28 q^{49} + 2 q^{50} + 32 q^{53} + 34 q^{56} - 48 q^{57} + 40 q^{58} + 28 q^{60} + 2 q^{64} + 8 q^{65} + 16 q^{70} + 62 q^{72} + 4 q^{74} - 8 q^{77} - 36 q^{78} - 24 q^{81} + 8 q^{84} - 28 q^{86} + 68 q^{88} + 4 q^{92} - 16 q^{93} + 30 q^{98} + O(q^{100})$$

## 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.g.a $4$ $1.118$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
140.2.g.b $4$ $1.118$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
140.2.g.c $8$ $1.118$ 8.0.342102016.5 None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$