# Properties

 Label 72.2.f Level $72$ Weight $2$ Character orbit 72.f Rep. character $\chi_{72}(35,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 72.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

## Trace form

 $$4 q + 4 q^{4} + O(q^{10})$$ $$4 q + 4 q^{4} - 12 q^{10} - 8 q^{16} - 16 q^{19} + 8 q^{22} + 4 q^{25} + 24 q^{28} - 4 q^{34} + 32 q^{43} + 24 q^{46} - 20 q^{49} - 24 q^{52} + 12 q^{58} - 32 q^{64} - 16 q^{67} - 24 q^{70} - 16 q^{73} - 16 q^{76} - 4 q^{82} + 32 q^{88} + 48 q^{91} - 24 q^{94} + 32 q^{97} + O(q^{100})$$

## 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.f.a $4$ $0.575$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

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

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