# Properties

 Label 72.8.d Level $72$ Weight $8$ Character orbit 72.d Rep. character $\chi_{72}(37,\cdot)$ Character field $\Q$ Dimension $34$ Newform subspaces $4$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$8$$ 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: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(72, [\chi])$$.

Total New Old
Modular forms 88 36 52
Cusp forms 80 34 46
Eisenstein series 8 2 6

## Trace form

 $$34 q + 8 q^{2} + 64 q^{4} - 688 q^{7} - 1084 q^{8} + O(q^{10})$$ $$34 q + 8 q^{2} + 64 q^{4} - 688 q^{7} - 1084 q^{8} - 4564 q^{10} - 16684 q^{14} + 12304 q^{16} + 1456 q^{17} - 60328 q^{20} - 95188 q^{22} + 144712 q^{23} - 476814 q^{25} - 108016 q^{26} + 122456 q^{28} + 446768 q^{31} + 76888 q^{32} + 26280 q^{34} - 150308 q^{38} + 769880 q^{40} - 79960 q^{41} - 178920 q^{44} - 2502408 q^{46} - 510024 q^{47} + 3805218 q^{49} - 175984 q^{50} - 2774976 q^{52} + 920752 q^{55} + 825224 q^{56} - 702676 q^{58} + 1288636 q^{62} - 8665040 q^{64} + 1103984 q^{65} - 2872200 q^{68} + 4761112 q^{70} + 2424408 q^{71} + 4623692 q^{73} - 1275400 q^{74} - 2285256 q^{76} + 6990368 q^{79} - 1768704 q^{80} + 273024 q^{82} + 900764 q^{86} + 7449584 q^{88} + 9783536 q^{89} - 11674080 q^{92} - 22068984 q^{94} + 20789440 q^{95} + 2997452 q^{97} - 38047296 q^{98} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.8.d.a $2$ $22.492$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$-1508$$ $$q+4\beta q^{2}-2^{7}q^{4}+197\beta q^{5}-754q^{7}+\cdots$$
72.8.d.b $6$ $22.492$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-6$$ $$0$$ $$0$$ $$-688$$ $$q+(-1-\beta _{1})q^{2}+(19+\beta _{1}+\beta _{3})q^{4}+\cdots$$
72.8.d.c $12$ $22.492$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$136$$ $$q+\beta _{1}q^{2}+(34+\beta _{3})q^{4}+(-3\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$$
72.8.d.d $14$ $22.492$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$14$$ $$0$$ $$0$$ $$1372$$ $$q+(1+\beta _{1})q^{2}+(-15+\beta _{1}-\beta _{2})q^{4}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(72, [\chi])$$ into lower level spaces

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