# Properties

 Label 120.2.r Level $120$ Weight $2$ Character orbit 120.r Rep. character $\chi_{120}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $3$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.r (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$7$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 64 12 52
Cusp forms 32 12 20
Eisenstein series 32 0 32

## Trace form

 $$12 q + 4 q^{7} + O(q^{10})$$ $$12 q + 4 q^{7} + 8 q^{13} - 12 q^{15} - 16 q^{21} - 8 q^{25} - 24 q^{27} - 8 q^{31} - 12 q^{33} - 32 q^{37} + 16 q^{45} + 48 q^{51} + 28 q^{55} + 40 q^{57} + 24 q^{61} + 44 q^{63} + 40 q^{67} + 20 q^{73} - 28 q^{81} - 48 q^{85} - 20 q^{87} - 80 q^{91} - 24 q^{93} - 44 q^{97} + O(q^{100})$$

## 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.r.a $4$ $0.958$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$12$$ $$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$$
120.2.r.b $4$ $0.958$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$$
120.2.r.c $4$ $0.958$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$4$$ $$-4$$ $$q+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(120, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(120, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$