# Properties

 Label 285.2.k Level $285$ Weight $2$ Character orbit 285.k Rep. character $\chi_{285}(77,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $72$ Newform subspaces $4$ Sturm bound $80$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 285.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$80$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(285, [\chi])$$.

Total New Old
Modular forms 88 72 16
Cusp forms 72 72 0
Eisenstein series 16 0 16

## Trace form

 $$72 q - 4 q^{3} - 8 q^{6} - 8 q^{7} + O(q^{10})$$ $$72 q - 4 q^{3} - 8 q^{6} - 8 q^{7} - 8 q^{10} + 16 q^{12} - 16 q^{13} - 16 q^{15} - 72 q^{16} - 8 q^{21} + 24 q^{22} - 24 q^{25} + 8 q^{27} + 8 q^{28} + 16 q^{30} + 16 q^{31} - 16 q^{33} + 8 q^{36} - 24 q^{37} + 24 q^{40} - 64 q^{42} - 16 q^{43} + 32 q^{46} - 12 q^{48} + 24 q^{51} + 72 q^{52} + 16 q^{55} - 72 q^{58} + 36 q^{60} - 64 q^{61} - 8 q^{63} + 40 q^{66} - 56 q^{67} + 64 q^{70} - 20 q^{72} + 40 q^{73} + 40 q^{75} + 16 q^{78} - 24 q^{81} - 88 q^{82} - 8 q^{85} + 168 q^{88} + 40 q^{90} - 32 q^{91} - 8 q^{93} - 48 q^{96} + 8 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(285, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.k.a $4$ $2.276$ $$\Q(\zeta_{12})$$ None $$-4$$ $$0$$ $$-4$$ $$-6$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots$$
285.2.k.b $4$ $2.276$ $$\Q(\zeta_{12})$$ None $$4$$ $$0$$ $$4$$ $$-6$$ $$q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
285.2.k.c $28$ $2.276$ None $$0$$ $$-2$$ $$0$$ $$0$$
285.2.k.d $36$ $2.276$ None $$0$$ $$-2$$ $$0$$ $$4$$