# Properties

 Label 72.2.i Level $72$ Weight $2$ Character orbit 72.i Rep. character $\chi_{72}(25,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 72.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

## Trace form

 $$6 q + q^{3} + 2 q^{5} - q^{9} + O(q^{10})$$ $$6 q + q^{3} + 2 q^{5} - q^{9} - 7 q^{11} - 14 q^{15} - 14 q^{17} + 6 q^{19} - 12 q^{21} - 4 q^{23} - 3 q^{25} + 16 q^{27} + 12 q^{29} - 6 q^{31} + 13 q^{33} + 36 q^{35} + 34 q^{39} + 9 q^{41} - 9 q^{43} + 2 q^{45} - 9 q^{49} - 19 q^{51} - 16 q^{53} - 12 q^{55} - 13 q^{57} - 25 q^{59} - 6 q^{61} - 18 q^{63} + 14 q^{65} - 3 q^{67} + 22 q^{69} - 8 q^{71} - 18 q^{73} - 19 q^{75} + 12 q^{77} + 6 q^{79} + 11 q^{81} - 26 q^{83} + 12 q^{85} - 24 q^{87} - 12 q^{89} + 12 q^{91} - 10 q^{93} + 16 q^{95} + 21 q^{97} + 20 q^{99} + O(q^{100})$$

## 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.i.a $2$ $0.575$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$3$$ $$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$$
72.2.i.b $4$ $0.575$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$1$$ $$-3$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(72, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$