# Properties

 Label 280.3.c Level $280$ Weight $3$ Character orbit 280.c Rep. character $\chi_{280}(69,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $7$ Sturm bound $144$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 280.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$280$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$17$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(280, [\chi])$$.

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

## Trace form

 $$92q - 4q^{4} - 260q^{9} + O(q^{10})$$ $$92q - 4q^{4} - 260q^{9} - 20q^{14} + 32q^{15} + 20q^{16} - 4q^{25} - 84q^{30} - 132q^{36} + 64q^{39} - 40q^{44} - 224q^{46} - 4q^{49} + 156q^{50} + 92q^{56} - 292q^{60} + 140q^{64} + 96q^{65} + 72q^{70} + 248q^{71} + 144q^{74} - 8q^{79} + 572q^{81} + 408q^{84} + 96q^{86} + 280q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
280.3.c.a $$1$$ $$7.629$$ $$\Q$$ $$\Q(\sqrt{-70})$$ $$-2$$ $$0$$ $$-5$$ $$-7$$ $$q-2q^{2}+4q^{4}-5q^{5}-7q^{7}-8q^{8}+\cdots$$
280.3.c.b $$1$$ $$7.629$$ $$\Q$$ $$\Q(\sqrt{-70})$$ $$-2$$ $$0$$ $$5$$ $$7$$ $$q-2q^{2}+4q^{4}+5q^{5}+7q^{7}-8q^{8}+\cdots$$
280.3.c.c $$1$$ $$7.629$$ $$\Q$$ $$\Q(\sqrt{-70})$$ $$2$$ $$0$$ $$-5$$ $$7$$ $$q+2q^{2}+4q^{4}-5q^{5}+7q^{7}+8q^{8}+\cdots$$
280.3.c.d $$1$$ $$7.629$$ $$\Q$$ $$\Q(\sqrt{-70})$$ $$2$$ $$0$$ $$5$$ $$-7$$ $$q+2q^{2}+4q^{4}+5q^{5}-7q^{7}+8q^{8}+\cdots$$
280.3.c.e $$4$$ $$7.629$$ $$\Q(i, \sqrt{14})$$ $$\Q(\sqrt{-14})$$ $$0$$ $$0$$ $$-12$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}-4q^{4}+\cdots$$
280.3.c.f $$4$$ $$7.629$$ $$\Q(i, \sqrt{14})$$ $$\Q(\sqrt{-14})$$ $$0$$ $$0$$ $$12$$ $$0$$ $$q-2\beta _{2}q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}-4q^{4}+\cdots$$
280.3.c.g $$80$$ $$7.629$$ None $$0$$ $$0$$ $$0$$ $$0$$