# Properties

 Label 280.2.bj Level $280$ Weight $2$ Character orbit 280.bj Rep. character $\chi_{280}(131,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $6$ Sturm bound $96$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

## Trace form

 $$64 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 32 q^{9} + O(q^{10})$$ $$64 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 32 q^{9} + 8 q^{11} + 30 q^{12} - 18 q^{14} - 6 q^{16} - 48 q^{22} - 36 q^{24} - 32 q^{25} - 30 q^{26} + 2 q^{28} - 22 q^{32} - 60 q^{36} + 60 q^{38} + 2 q^{42} - 16 q^{43} - 14 q^{44} + 18 q^{46} + 16 q^{49} + 4 q^{50} - 40 q^{51} - 36 q^{52} + 72 q^{54} + 20 q^{56} + 32 q^{57} + 6 q^{58} - 48 q^{59} + 14 q^{60} + 52 q^{64} + 24 q^{66} - 40 q^{67} + 20 q^{70} - 40 q^{72} - 48 q^{73} + 14 q^{74} - 72 q^{78} - 24 q^{81} - 42 q^{82} - 88 q^{84} + 24 q^{86} + 16 q^{88} - 24 q^{89} + 64 q^{91} - 108 q^{92} + 54 q^{94} - 144 q^{96} + 10 q^{98} + 80 q^{99} + O(q^{100})$$

## 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.bj.a $4$ $2.236$ $$\Q(\zeta_{12})$$ None $$-4$$ $$-6$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2})q^{3}+\cdots$$
280.2.bj.b $4$ $2.236$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$-2$$ $$-10$$ $$q+\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$$
280.2.bj.c $4$ $2.236$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$2$$ $$10$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
280.2.bj.d $4$ $2.236$ $$\Q(\zeta_{12})$$ None $$2$$ $$-6$$ $$2$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
280.2.bj.e $24$ $2.236$ None $$-3$$ $$12$$ $$12$$ $$-10$$
280.2.bj.f $24$ $2.236$ None $$3$$ $$12$$ $$-12$$ $$10$$

## Decomposition of $$S_{2}^{\mathrm{old}}(280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$