# Properties

 Label 270.2.c Level $270$ Weight $2$ Character orbit 270.c Rep. character $\chi_{270}(109,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $3$ Sturm bound $108$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$270 = 2 \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 270.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$108$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(270, [\chi])$$.

Total New Old
Modular forms 66 8 58
Cusp forms 42 8 34
Eisenstein series 24 0 24

## Trace form

 $$8 q - 8 q^{4} + O(q^{10})$$ $$8 q - 8 q^{4} + 10 q^{10} + 8 q^{16} + 6 q^{25} + 8 q^{31} - 20 q^{34} - 10 q^{40} - 4 q^{46} - 84 q^{49} + 58 q^{55} + 16 q^{61} - 8 q^{64} + 22 q^{70} - 36 q^{79} + 16 q^{85} - 48 q^{91} + 44 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(270, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.2.c.a $2$ $2.156$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots$$
270.2.c.b $2$ $2.156$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots$$
270.2.c.c $4$ $2.156$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(270, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(270, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 2}$$