# Properties

 Label 280.2.bv Level $280$ Weight $2$ Character orbit 280.bv Rep. character $\chi_{280}(117,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $176$ Newform subspaces $5$ Sturm bound $96$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.bv (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$280$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(280, [\chi])$$.

Total New Old
Modular forms 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

## Trace form

 $$176q - 2q^{2} - 8q^{7} + 4q^{8} + O(q^{10})$$ $$176q - 2q^{2} - 8q^{7} + 4q^{8} - 6q^{10} - 6q^{12} - 16q^{15} - 12q^{16} - 12q^{17} - 16q^{18} - 16q^{22} - 4q^{23} - 4q^{25} - 12q^{26} - 50q^{28} + 8q^{30} - 24q^{31} + 18q^{32} - 12q^{33} - 48q^{36} - 24q^{38} + 54q^{40} - 10q^{42} - 28q^{46} - 84q^{47} - 12q^{50} + 72q^{52} - 20q^{56} - 40q^{57} + 2q^{58} + 46q^{60} - 24q^{63} - 4q^{65} - 156q^{66} + 60q^{68} - 112q^{70} + 32q^{71} + 52q^{72} - 12q^{73} - 24q^{78} + 48q^{80} - 54q^{82} - 72q^{86} - 48q^{87} + 60q^{88} + 12q^{92} - 20q^{95} - 96q^{96} - 130q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
280.2.bv.a $$4$$ $$2.236$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$-2$$ $$-4$$ $$-10$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$$
280.2.bv.b $$4$$ $$2.236$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$2$$ $$4$$ $$-10$$ $$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$$
280.2.bv.c $$4$$ $$2.236$$ $$\Q(\zeta_{12})$$ None $$2$$ $$-4$$ $$4$$ $$0$$ $$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots$$
280.2.bv.d $$4$$ $$2.236$$ $$\Q(\zeta_{12})$$ None $$4$$ $$4$$ $$-4$$ $$0$$ $$q+(1-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
280.2.bv.e $$160$$ $$2.236$$ None $$-2$$ $$0$$ $$0$$ $$12$$