# Properties

 Label 72.2.n Level $72$ Weight $2$ Character orbit 72.n Rep. character $\chi_{72}(13,\cdot)$ 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.n (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

 $$20 q - q^{2} - q^{4} - q^{6} - 2 q^{7} - 10 q^{8} - 4 q^{9} + O(q^{10})$$ $$20 q - q^{2} - q^{4} - q^{6} - 2 q^{7} - 10 q^{8} - 4 q^{9} - 8 q^{10} - 16 q^{12} + 8 q^{14} - 10 q^{15} - q^{16} - 8 q^{17} + 16 q^{18} - 16 q^{20} - 5 q^{22} - 14 q^{23} - 5 q^{24} + 20 q^{26} + 4 q^{28} + 34 q^{30} - 2 q^{31} + 19 q^{32} - 18 q^{33} - 9 q^{34} + 27 q^{36} + 25 q^{38} + 2 q^{39} - 2 q^{40} + 2 q^{41} + 8 q^{42} + 42 q^{44} - 12 q^{46} + 18 q^{47} + 39 q^{48} - 25 q^{50} - 47 q^{54} - 28 q^{55} + 26 q^{56} + 4 q^{57} - 14 q^{58} + 6 q^{60} - 68 q^{62} + 50 q^{63} + 26 q^{64} - 22 q^{65} - 72 q^{66} - 39 q^{68} - 16 q^{70} + 48 q^{71} - 65 q^{72} - 8 q^{73} - 34 q^{74} + 9 q^{76} - 2 q^{78} - 2 q^{79} - 96 q^{80} - 8 q^{81} + 18 q^{82} - 76 q^{84} + 29 q^{86} + 42 q^{87} + 19 q^{88} + 8 q^{89} + 52 q^{90} - 30 q^{92} + 40 q^{95} - 26 q^{96} - 2 q^{97} + 102 q^{98} + O(q^{100})$$

## 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.n.a $4$ $0.575$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$-8$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$$
72.2.n.b $16$ $0.575$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$1$$ $$0$$ $$0$$ $$6$$ $$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots$$