# Properties

 Label 72.1.p Level $72$ Weight $1$ Character orbit 72.p Rep. character $\chi_{72}(43,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 72.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(72, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{8} - q^{9} + O(q^{10})$$ $$2 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{8} - q^{9} + q^{11} + 2 q^{12} - q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} + q^{22} - q^{24} - q^{25} + 2 q^{27} - q^{32} + q^{33} + q^{34} - q^{36} + q^{38} + q^{41} + q^{43} - 2 q^{44} - q^{48} - q^{49} - q^{50} + q^{51} - q^{54} + q^{57} + q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - q^{72} - 2 q^{73} - q^{75} + q^{76} - q^{81} - 2 q^{82} - 2 q^{83} + q^{86} + q^{88} + 4 q^{89} + 2 q^{96} + q^{97} + 2 q^{98} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.1.p.a $2$ $0.036$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$-1$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$$