# Properties

 Label 60.3.k Level $60$ Weight $3$ Character orbit 60.k Rep. character $\chi_{60}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 60.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(60, [\chi])$$.

Total New Old
Modular forms 60 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

## Trace form

 $$4q + 12q^{5} + 20q^{7} + O(q^{10})$$ $$4q + 12q^{5} + 20q^{7} - 16q^{11} - 24q^{15} - 40q^{17} - 24q^{21} - 40q^{23} - 16q^{25} + 16q^{31} + 60q^{33} + 56q^{35} + 200q^{41} + 120q^{43} - 12q^{45} - 24q^{51} - 200q^{53} - 108q^{55} + 120q^{57} - 312q^{61} + 60q^{63} + 240q^{65} - 40q^{67} - 80q^{71} - 20q^{73} - 168q^{75} - 200q^{77} - 36q^{81} - 240q^{83} - 184q^{85} + 60q^{87} + 240q^{91} + 120q^{93} + 400q^{95} + 300q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(60, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
60.3.k.a $$4$$ $$1.635$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$12$$ $$20$$ $$q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(60, [\chi])$$ into lower level spaces

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