# Properties

 Label 60.2.h Level $60$ Weight $2$ Character orbit 60.h Rep. character $\chi_{60}(59,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $24$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 60.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$60$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(60, [\chi])$$.

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

## Trace form

 $$8 q - 6 q^{4} + 2 q^{6} - 4 q^{9} + O(q^{10})$$ $$8 q - 6 q^{4} + 2 q^{6} - 4 q^{9} - 10 q^{10} + 2 q^{16} - 20 q^{21} + 26 q^{24} + 20 q^{30} + 20 q^{34} - 22 q^{36} + 10 q^{40} + 20 q^{45} - 4 q^{46} - 16 q^{49} - 46 q^{54} - 30 q^{60} + 24 q^{61} - 54 q^{64} + 28 q^{69} - 40 q^{70} + 60 q^{76} + 32 q^{81} + 40 q^{84} - 40 q^{85} + 30 q^{90} + 92 q^{94} - 22 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(60, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.2.h.a $4$ $0.479$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots$$
60.2.h.b $4$ $0.479$ $$\Q(\sqrt{-3}, \sqrt{5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots$$