# Properties

 Label 285.2.c Level $285$ Weight $2$ Character orbit 285.c Rep. character $\chi_{285}(229,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ 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 44 20 24
Cusp forms 36 20 16
Eisenstein series 8 0 8

## Trace form

 $$20 q - 24 q^{4} + 2 q^{5} + 4 q^{6} - 20 q^{9} + O(q^{10})$$ $$20 q - 24 q^{4} + 2 q^{5} + 4 q^{6} - 20 q^{9} - 12 q^{10} + 4 q^{11} + 16 q^{14} - 4 q^{15} + 32 q^{16} - 8 q^{19} - 12 q^{24} - 2 q^{25} - 32 q^{26} + 16 q^{29} + 8 q^{30} - 8 q^{31} + 8 q^{34} - 6 q^{35} + 24 q^{36} - 8 q^{39} + 16 q^{40} + 24 q^{41} + 48 q^{44} - 2 q^{45} - 16 q^{46} - 48 q^{49} - 20 q^{50} - 8 q^{51} - 4 q^{54} + 14 q^{55} - 24 q^{56} + 48 q^{59} - 8 q^{60} + 4 q^{61} - 4 q^{65} + 24 q^{66} + 8 q^{69} - 36 q^{70} - 48 q^{71} - 56 q^{74} + 8 q^{75} + 20 q^{76} + 4 q^{80} + 20 q^{81} - 32 q^{84} - 6 q^{85} - 32 q^{86} - 16 q^{89} + 12 q^{90} + 40 q^{91} + 8 q^{94} - 2 q^{95} + 68 q^{96} - 4 q^{99} + O(q^{100})$$

## 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.c.a $6$ $2.276$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$$
285.2.c.b $14$ $2.276$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$$

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

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