# Properties

 Label 120.3.u Level $120$ Weight $3$ Character orbit 120.u Rep. character $\chi_{120}(73,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 120.u (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(120, [\chi])$$.

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

## Trace form

 $$12q - 8q^{5} - 8q^{7} + O(q^{10})$$ $$12q - 8q^{5} - 8q^{7} + 16q^{11} + 44q^{13} + 24q^{15} + 28q^{17} - 96q^{23} - 68q^{25} + 16q^{31} + 72q^{33} + 52q^{37} - 208q^{41} - 96q^{43} - 36q^{45} - 32q^{47} - 12q^{53} + 136q^{55} - 96q^{57} + 240q^{61} - 24q^{63} + 20q^{65} - 224q^{67} + 32q^{71} - 100q^{73} + 96q^{75} + 240q^{77} - 108q^{81} + 608q^{83} + 60q^{85} + 360q^{87} + 256q^{91} + 144q^{93} - 32q^{95} - 356q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(120, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
120.3.u.a $$4$$ $$3.270$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$4$$ $$-12$$ $$q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots$$
120.3.u.b $$8$$ $$3.270$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$4$$ $$q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(120, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(120, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$