# 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

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

## 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

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