# Properties

 Label 60.3.g Level $60$ Weight $3$ Character orbit 60.g Rep. character $\chi_{60}(41,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 60.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ 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 30 2 28
Cusp forms 18 2 16
Eisenstein series 12 0 12

## Trace form

 $$2 q + 4 q^{3} + 4 q^{7} - 2 q^{9} + O(q^{10})$$ $$2 q + 4 q^{3} + 4 q^{7} - 2 q^{9} + 16 q^{13} - 10 q^{15} - 68 q^{19} + 8 q^{21} - 10 q^{25} - 44 q^{27} + 28 q^{31} + 60 q^{33} + 112 q^{37} + 32 q^{39} + 16 q^{43} - 40 q^{45} - 90 q^{49} + 60 q^{51} + 60 q^{55} - 136 q^{57} - 92 q^{61} - 4 q^{63} + 64 q^{67} + 180 q^{69} - 212 q^{73} - 20 q^{75} - 44 q^{79} - 158 q^{81} + 60 q^{85} - 180 q^{87} + 32 q^{91} + 56 q^{93} + 244 q^{97} + 240 q^{99} + O(q^{100})$$

## 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.g.a $2$ $1.635$ $$\Q(\sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$4$$ $$q+(2+\beta )q^{3}+\beta q^{5}+2q^{7}+(-1+4\beta )q^{9}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(60, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$