# Properties

 Label 560.5.p Level $560$ Weight $5$ Character orbit 560.p Rep. character $\chi_{560}(209,\cdot)$ Character field $\Q$ Dimension $94$ Newform subspaces $10$ Sturm bound $480$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 560.p (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$480$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(560, [\chi])$$.

Total New Old
Modular forms 396 98 298
Cusp forms 372 94 278
Eisenstein series 24 4 20

## Trace form

 $$94 q + 2426 q^{9} + O(q^{10})$$ $$94 q + 2426 q^{9} + 4 q^{11} + 164 q^{15} - 468 q^{21} - 738 q^{25} + 1052 q^{29} - 958 q^{35} - 2648 q^{39} - 1650 q^{49} + 3976 q^{51} + 3260 q^{65} + 10276 q^{71} + 27268 q^{79} + 44086 q^{81} + 1404 q^{85} + 31108 q^{91} - 25440 q^{95} + 37708 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(560, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
560.5.p.a $$1$$ $$57.887$$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-17$$ $$-25$$ $$49$$ $$q-17q^{3}-5^{2}q^{5}+7^{2}q^{7}+208q^{9}+\cdots$$
560.5.p.b $$1$$ $$57.887$$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$17$$ $$25$$ $$-49$$ $$q+17q^{3}+5^{2}q^{5}-7^{2}q^{7}+208q^{9}+\cdots$$
560.5.p.c $$2$$ $$57.887$$ $$\Q(\sqrt{105})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-17$$ $$50$$ $$-98$$ $$q+(-8-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(9+\cdots)q^{9}+\cdots$$
560.5.p.d $$2$$ $$57.887$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$-10$$ $$10$$ $$-70$$ $$q-5q^{3}+(5+5\beta )q^{5}+(-35+7\beta )q^{7}+\cdots$$
560.5.p.e $$2$$ $$57.887$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$10$$ $$-10$$ $$70$$ $$q+5q^{3}+(-5-5\beta )q^{5}+(35+7\beta )q^{7}+\cdots$$
560.5.p.f $$2$$ $$57.887$$ $$\Q(\sqrt{105})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$17$$ $$-50$$ $$98$$ $$q+(9-\beta )q^{3}-5^{2}q^{5}+7^{2}q^{7}+(26-17\beta )q^{9}+\cdots$$
560.5.p.g $$8$$ $$57.887$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-3\beta _{2}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
560.5.p.h $$12$$ $$57.887$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{3}+(\beta _{1}+\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots$$
560.5.p.i $$16$$ $$57.887$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{8}q^{7}+(29-\beta _{10}+\cdots)q^{9}+\cdots$$
560.5.p.j $$48$$ $$57.887$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{5}^{\mathrm{old}}(560, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(560, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$