# Properties

 Label 15.8.b Level 15 Weight 8 Character orbit b Rep. character $$\chi_{15}(4,\cdot)$$ Character field $$\Q$$ Dimension 8 Newforms 1 Sturm bound 16 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$15 = 3 \cdot 5$$ Weight: $$k$$ = $$8$$ Character orbit: $$[\chi]$$ = 15.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$5$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(15, [\chi])$$.

Total New Old
Modular forms 16 8 8
Cusp forms 12 8 4
Eisenstein series 4 0 4

## Trace form

 $$8q - 666q^{4} - 444q^{5} + 486q^{6} - 5832q^{9} + O(q^{10})$$ $$8q - 666q^{4} - 444q^{5} + 486q^{6} - 5832q^{9} - 6686q^{10} + 10752q^{11} - 13524q^{14} - 17496q^{15} + 86530q^{16} - 30464q^{19} + 87444q^{20} + 64152q^{21} - 110322q^{24} + 127616q^{25} - 793524q^{26} + 240072q^{29} - 172044q^{30} + 233728q^{31} + 184748q^{34} + 593520q^{35} + 485514q^{36} - 454896q^{39} - 1147102q^{40} + 507648q^{41} + 2578572q^{44} + 323676q^{45} + 662408q^{46} - 3267160q^{49} - 5117736q^{50} + 264384q^{51} - 354294q^{54} + 3525696q^{55} + 705660q^{56} + 1091424q^{59} + 5307606q^{60} - 6433520q^{61} - 568594q^{64} - 2555592q^{65} - 2382372q^{66} - 5940864q^{69} + 12097800q^{70} - 1381824q^{71} + 23961276q^{74} + 7768224q^{75} + 13115664q^{76} - 14380160q^{79} - 31251876q^{80} + 4251528q^{81} - 36423756q^{84} - 1452008q^{85} - 19837608q^{86} + 45778896q^{89} + 4874094q^{90} + 24075648q^{91} - 45728896q^{94} - 25774656q^{95} + 33586002q^{96} - 7838208q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(15, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
15.8.b.a $$8$$ $$4.686$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$-444$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(15, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(15, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$