# Properties

 Label 60.3.f Level $60$ Weight $3$ Character orbit 60.f Rep. character $\chi_{60}(19,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 60.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

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

## Trace form

 $$12q - 2q^{4} + 4q^{5} + 6q^{6} + 36q^{9} + O(q^{10})$$ $$12q - 2q^{4} + 4q^{5} + 6q^{6} + 36q^{9} - 22q^{10} - 52q^{14} - 78q^{16} + 52q^{20} - 18q^{24} - 68q^{25} + 156q^{26} - 40q^{29} - 60q^{30} - 28q^{34} - 6q^{36} + 154q^{40} - 184q^{41} + 204q^{44} + 12q^{45} + 160q^{46} + 212q^{49} + 72q^{50} + 18q^{54} - 244q^{56} + 126q^{60} + 8q^{61} - 266q^{64} - 192q^{65} - 84q^{66} - 96q^{69} - 104q^{70} - 468q^{74} + 168q^{76} - 308q^{80} + 108q^{81} - 348q^{84} + 224q^{85} - 136q^{86} + 632q^{89} - 66q^{90} + 376q^{94} + 234q^{96} + O(q^{100})$$

## 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.f.a $$4$$ $$1.635$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
60.3.f.b $$8$$ $$1.635$$ 8.0.$$\cdots$$.4 None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$$

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

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