Properties

 Label 72.4.d Level $72$ Weight $4$ Character orbit 72.d Rep. character $\chi_{72}(37,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $4$ Sturm bound $48$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 72.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(72, [\chi])$$.

Total New Old
Modular forms 40 16 24
Cusp forms 32 14 18
Eisenstein series 8 2 6

Trace form

 $$14 q - 16 q^{7} + 36 q^{8} + O(q^{10})$$ $$14 q - 16 q^{7} + 36 q^{8} + 76 q^{10} + 84 q^{14} + 16 q^{16} - 24 q^{17} - 168 q^{20} - 132 q^{22} - 24 q^{23} - 274 q^{25} - 336 q^{26} + 408 q^{28} - 80 q^{31} + 600 q^{32} + 184 q^{34} + 972 q^{38} - 1000 q^{40} - 96 q^{41} - 1320 q^{44} - 776 q^{46} - 264 q^{47} + 750 q^{49} - 1944 q^{50} + 832 q^{52} - 48 q^{55} + 2184 q^{56} + 2124 q^{58} + 2556 q^{62} - 1488 q^{64} + 624 q^{65} - 3144 q^{68} - 2408 q^{70} + 1848 q^{71} - 156 q^{73} - 2856 q^{74} + 2168 q^{76} + 2144 q^{79} + 3456 q^{80} + 1424 q^{82} + 3084 q^{86} - 912 q^{88} - 312 q^{89} - 3552 q^{92} - 2808 q^{94} - 4320 q^{95} - 1084 q^{97} - 3912 q^{98} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.4.d.a $2$ $4.248$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$-68$$ $$q+\beta q^{2}-8q^{4}-7\beta q^{5}-34q^{7}-8\beta q^{8}+\cdots$$
72.4.d.b $2$ $4.248$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$-16$$ $$q+(1+\beta )q^{2}+(-6+2\beta )q^{4}+4\beta q^{5}+\cdots$$
72.4.d.c $4$ $4.248$ $$\Q(\sqrt{-10}, \sqrt{22})$$ None $$0$$ $$0$$ $$0$$ $$40$$ $$q+\beta _{1}q^{2}+(3+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$$
72.4.d.d $6$ $4.248$ 6.0.8248384.1 None $$-2$$ $$0$$ $$0$$ $$28$$ $$q+\beta _{1}q^{2}+(3+\beta _{5})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(72, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(72, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$