# Properties

 Label 72.2.l Level $72$ Weight $2$ Character orbit 72.l Rep. character $\chi_{72}(11,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ 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.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ 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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

## Trace form

 $$20 q - 3 q^{2} - 4 q^{3} - q^{4} - 7 q^{6} - 4 q^{9} + O(q^{10})$$ $$20 q - 3 q^{2} - 4 q^{3} - q^{4} - 7 q^{6} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 18 q^{14} - q^{16} - 16 q^{18} - 8 q^{19} + 18 q^{20} - 5 q^{22} + 29 q^{24} - 4 q^{25} - 16 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32} - 2 q^{33} - 5 q^{34} + 23 q^{36} + 21 q^{38} - 12 q^{40} - 18 q^{41} + 42 q^{42} - 2 q^{43} + 12 q^{46} - 19 q^{48} - 4 q^{49} + 51 q^{50} + 28 q^{51} - 18 q^{52} + 35 q^{54} - 66 q^{56} - 20 q^{57} + 12 q^{58} + 30 q^{59} - 72 q^{60} + 2 q^{64} - 6 q^{65} - 32 q^{66} - 2 q^{67} - 45 q^{68} + 18 q^{70} - 37 q^{72} - 8 q^{73} - 60 q^{74} + 68 q^{75} - 11 q^{76} - 72 q^{78} + 8 q^{81} + 10 q^{82} + 54 q^{83} + 12 q^{84} - 87 q^{86} - 5 q^{88} - 66 q^{90} - 36 q^{91} + 84 q^{92} + 24 q^{94} + 74 q^{96} - 2 q^{97} + 10 q^{99} + O(q^{100})$$

## 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.l.a $4$ $0.575$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
72.2.l.b $16$ $0.575$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-3$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$