# Properties

 Label 285.2.u Level $285$ Weight $2$ Character orbit 285.u Rep. character $\chi_{285}(16,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $84$ Newform subspaces $4$ Sturm bound $80$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 285.u (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$4$$ Sturm bound: $$80$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 264 84 180
Cusp forms 216 84 132
Eisenstein series 48 0 48

## Trace form

 $$84 q + 6 q^{4} + 6 q^{6} + O(q^{10})$$ $$84 q + 6 q^{4} + 6 q^{6} + 6 q^{10} + 12 q^{12} + 18 q^{13} - 24 q^{14} - 18 q^{16} + 6 q^{19} + 18 q^{21} + 24 q^{22} - 24 q^{23} - 24 q^{24} - 12 q^{26} + 6 q^{27} + 12 q^{28} - 48 q^{29} - 24 q^{31} - 120 q^{32} - 90 q^{34} + 12 q^{35} + 6 q^{36} + 84 q^{38} + 12 q^{40} - 12 q^{41} + 24 q^{42} + 18 q^{43} - 84 q^{44} - 60 q^{46} - 36 q^{47} + 48 q^{48} - 78 q^{49} + 12 q^{51} + 36 q^{52} + 72 q^{53} + 6 q^{54} + 144 q^{56} - 48 q^{58} + 12 q^{59} - 12 q^{60} + 36 q^{61} + 168 q^{62} - 12 q^{63} - 18 q^{64} - 36 q^{65} - 96 q^{66} - 18 q^{67} - 12 q^{68} - 24 q^{69} - 72 q^{70} - 72 q^{71} + 66 q^{73} - 60 q^{74} - 12 q^{75} + 24 q^{76} + 72 q^{77} - 120 q^{78} + 48 q^{79} - 96 q^{80} + 84 q^{82} - 48 q^{83} - 36 q^{84} - 48 q^{85} - 168 q^{86} + 24 q^{88} + 48 q^{89} - 12 q^{90} - 12 q^{91} + 48 q^{92} + 24 q^{96} + 60 q^{97} + 192 q^{98} + 12 q^{99} + O(q^{100})$$

## 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.u.a $12$ $2.276$ 12.0.$$\cdots$$.1 None $$3$$ $$0$$ $$0$$ $$6$$ $$q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+\beta _{10}q^{3}+\cdots$$
285.2.u.b $18$ $2.276$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-3$$ $$0$$ $$0$$ $$6$$ $$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-\beta _{2}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots$$
285.2.u.c $24$ $2.276$ None $$0$$ $$0$$ $$0$$ $$-6$$
285.2.u.d $30$ $2.276$ None $$0$$ $$0$$ $$0$$ $$-6$$

## Decomposition of $$S_{2}^{\mathrm{old}}(285, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(285, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 2}$$