# Properties

 Label 72.2.d Level $72$ Weight $2$ Character orbit 72.d Rep. character $\chi_{72}(37,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 72.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(72, [\chi])$$.

Total New Old
Modular forms 16 6 10
Cusp forms 8 4 4
Eisenstein series 8 2 6

## Trace form

 $$4 q + 2 q^{2} - 4 q^{4} - 4 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{10} - 4 q^{14} + 4 q^{17} + 8 q^{20} + 16 q^{22} - 8 q^{23} - 4 q^{25} + 8 q^{26} - 8 q^{28} - 16 q^{31} - 8 q^{32} + 4 q^{34} - 8 q^{38} + 24 q^{40} - 4 q^{41} - 8 q^{46} + 24 q^{47} - 12 q^{49} + 2 q^{50} + 16 q^{52} + 32 q^{55} + 8 q^{56} - 20 q^{58} + 4 q^{62} - 16 q^{64} - 16 q^{65} - 24 q^{70} - 24 q^{71} + 16 q^{73} - 16 q^{74} - 16 q^{76} - 4 q^{82} + 8 q^{86} - 32 q^{88} + 20 q^{89} + 24 q^{94} + 16 q^{95} - 6 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.2.d.a $2$ $0.575$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta q^{2}-2q^{4}+2\beta q^{5}+2q^{7}-2\beta q^{8}+\cdots$$
72.2.d.b $2$ $0.575$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+(1+i)q^{2}+2iq^{4}-2iq^{5}-2q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(72, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(72, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$