# Properties

 Label 285.2.i Level $285$ Weight $2$ Character orbit 285.i Rep. character $\chi_{285}(106,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $6$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ 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 24 64
Cusp forms 72 24 48
Eisenstein series 16 0 16

## Trace form

 $$24 q + 4 q^{3} - 10 q^{4} - 2 q^{6} + 8 q^{7} - 12 q^{9} + O(q^{10})$$ $$24 q + 4 q^{3} - 10 q^{4} - 2 q^{6} + 8 q^{7} - 12 q^{9} + 2 q^{10} + 8 q^{11} - 24 q^{12} + 12 q^{14} + 4 q^{15} - 6 q^{16} - 12 q^{17} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 12 q^{25} + 40 q^{26} - 8 q^{27} + 28 q^{28} - 16 q^{31} + 20 q^{32} + 8 q^{33} - 26 q^{34} - 4 q^{35} - 10 q^{36} - 16 q^{37} - 20 q^{38} + 16 q^{39} + 12 q^{40} - 20 q^{41} - 8 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{46} - 12 q^{47} + 12 q^{48} + 48 q^{49} - 4 q^{51} - 32 q^{52} - 8 q^{53} - 2 q^{54} + 24 q^{56} + 20 q^{57} + 104 q^{58} + 4 q^{59} + 6 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 40 q^{64} - 48 q^{65} + 16 q^{66} + 8 q^{67} - 40 q^{68} - 16 q^{69} - 4 q^{70} - 8 q^{71} - 8 q^{73} + 36 q^{74} - 8 q^{75} - 60 q^{76} + 16 q^{77} - 12 q^{78} + 8 q^{79} - 16 q^{80} - 12 q^{81} + 60 q^{82} - 40 q^{83} - 8 q^{84} - 8 q^{85} - 20 q^{86} + 16 q^{87} + 16 q^{88} - 36 q^{89} + 2 q^{90} - 20 q^{91} + 56 q^{92} - 12 q^{93} + 68 q^{94} + 16 q^{95} + 44 q^{96} + 20 q^{97} - 64 q^{98} - 4 q^{99} + O(q^{100})$$

## 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.i.a $2$ $2.276$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-1$$ $$1$$ $$-4$$ $$q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
285.2.i.b $2$ $2.276$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$$
285.2.i.c $2$ $2.276$ $$\Q(\sqrt{-3})$$ None $$2$$ $$1$$ $$1$$ $$-4$$ $$q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
285.2.i.d $4$ $2.276$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots$$
285.2.i.e $4$ $2.276$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$1$$ $$-2$$ $$2$$ $$12$$ $$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
285.2.i.f $10$ $2.276$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$1$$ $$5$$ $$-5$$ $$4$$ $$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{4}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$$

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

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