# Properties

 Label 270.3.j Level $270$ Weight $3$ Character orbit 270.j Rep. character $\chi_{270}(89,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $2$ Sturm bound $162$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$270 = 2 \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 270.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$162$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(270, [\chi])$$.

Total New Old
Modular forms 240 24 216
Cusp forms 192 24 168
Eisenstein series 48 0 48

## Trace form

 $$24 q - 24 q^{4} - 18 q^{5} + O(q^{10})$$ $$24 q - 24 q^{4} - 18 q^{5} - 36 q^{11} + 36 q^{14} - 48 q^{16} + 36 q^{20} - 6 q^{25} - 36 q^{29} - 60 q^{31} + 144 q^{41} - 24 q^{46} + 108 q^{49} - 288 q^{50} - 156 q^{55} - 72 q^{56} + 36 q^{59} + 48 q^{61} + 192 q^{64} + 414 q^{65} + 48 q^{70} - 144 q^{74} + 132 q^{79} + 48 q^{85} + 432 q^{86} + 168 q^{91} - 84 q^{94} - 540 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(270, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.3.j.a $8$ $7.357$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots$$
270.3.j.b $16$ $7.357$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-30$$ $$0$$ $$q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(270, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(270, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 2}$$