# Properties

 Label 731.2.m Level 731 Weight 2 Character orbit m Rep. character $$\chi_{731}(87,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 248 Newforms 3 Sturm bound 132 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$731 = 17 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 731.m (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$17$$ Character field: $$\Q(\zeta_{8})$$ Newforms: $$3$$ Sturm bound: $$132$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(731, [\chi])$$.

Total New Old
Modular forms 272 248 24
Cusp forms 256 248 8
Eisenstein series 16 0 16

## Trace form

 $$248q - 16q^{6} + O(q^{10})$$ $$248q - 16q^{6} - 16q^{10} + 16q^{14} + 8q^{15} - 224q^{16} - 8q^{17} + 32q^{18} - 24q^{19} + 16q^{20} - 32q^{22} - 20q^{23} - 24q^{24} - 8q^{25} - 16q^{26} + 48q^{28} - 32q^{33} + 64q^{34} - 64q^{35} + 64q^{36} - 40q^{37} + 16q^{39} + 96q^{40} + 16q^{41} + 8q^{42} + 48q^{44} - 64q^{45} - 80q^{46} + 80q^{48} + 16q^{49} - 64q^{51} - 48q^{52} + 4q^{53} - 72q^{54} + 120q^{56} - 32q^{57} - 64q^{58} + 16q^{59} - 48q^{60} - 16q^{61} - 88q^{62} + 40q^{63} + 40q^{65} - 120q^{66} + 16q^{67} + 96q^{69} - 8q^{70} + 40q^{73} + 16q^{74} + 72q^{75} - 32q^{76} + 56q^{77} - 48q^{78} - 16q^{79} - 88q^{80} + 104q^{82} - 104q^{83} - 16q^{84} + 24q^{85} - 40q^{86} + 72q^{88} + 16q^{90} + 80q^{91} - 32q^{92} - 152q^{93} - 16q^{94} + 72q^{95} + 120q^{96} - 16q^{97} - 48q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(731, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
731.2.m.a $$4$$ $$5.837$$ $$\Q(\zeta_{8})$$ None $$-4$$ $$-4$$ $$-8$$ $$-4$$ $$q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$$
731.2.m.b $$116$$ $$5.837$$ None $$0$$ $$0$$ $$0$$ $$0$$
731.2.m.c $$128$$ $$5.837$$ None $$4$$ $$4$$ $$8$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(731, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(731, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(17, [\chi])$$$$^{\oplus 2}$$