# Properties

 Label 120.2.w Level $120$ Weight $2$ Character orbit 120.w Rep. character $\chi_{120}(53,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $3$ Sturm bound $48$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.w (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$120$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(120, [\chi])$$.

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

## Trace form

 $$40 q - 4 q^{6} - 8 q^{7} + O(q^{10})$$ $$40 q - 4 q^{6} - 8 q^{7} - 12 q^{10} - 8 q^{12} - 4 q^{15} - 4 q^{16} - 20 q^{18} - 20 q^{22} - 8 q^{25} + 28 q^{28} - 32 q^{30} - 32 q^{31} - 16 q^{33} + 28 q^{36} + 24 q^{40} - 32 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} - 48 q^{55} - 16 q^{57} + 44 q^{58} + 56 q^{60} + 24 q^{63} + 16 q^{66} + 84 q^{70} + 32 q^{72} - 8 q^{73} - 88 q^{76} + 64 q^{78} - 24 q^{81} + 64 q^{82} + 64 q^{87} - 116 q^{88} + 84 q^{90} - 52 q^{96} + 8 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(120, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.2.w.a $4$ $0.958$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-6})$$ $$-4$$ $$0$$ $$4$$ $$-4$$ $$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$$
120.2.w.b $4$ $0.958$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-6})$$ $$4$$ $$0$$ $$-4$$ $$-4$$ $$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
120.2.w.c $32$ $0.958$ None $$0$$ $$0$$ $$0$$ $$0$$