# Properties

 Label 3360.2.j Level $3360$ Weight $2$ Character orbit 3360.j Rep. character $\chi_{3360}(1009,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $6$ Sturm bound $1536$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3360.j (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1536$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3360, [\chi])$$.

Total New Old
Modular forms 800 72 728
Cusp forms 736 72 664
Eisenstein series 64 0 64

## Trace form

 $$72 q + 72 q^{9} + O(q^{10})$$ $$72 q + 72 q^{9} - 8 q^{25} - 16 q^{31} - 32 q^{39} + 16 q^{41} - 72 q^{49} - 32 q^{55} + 48 q^{65} + 64 q^{79} + 72 q^{81} + 80 q^{89} + 80 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3360, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3360.2.j.a $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q-q^{3}+(-2+i)q^{5}-iq^{7}+q^{9}-6q^{13}+\cdots$$
3360.2.j.b $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$4$$ $$0$$ $$q-q^{3}+(2-i)q^{5}+iq^{7}+q^{9}+4iq^{11}+\cdots$$
3360.2.j.c $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-4$$ $$0$$ $$q+q^{3}+(-2-i)q^{5}-iq^{7}+q^{9}+4iq^{11}+\cdots$$
3360.2.j.d $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$0$$ $$q+q^{3}+(2+i)q^{5}+iq^{7}+q^{9}+6q^{13}+\cdots$$
3360.2.j.e $32$ $26.830$ None $$0$$ $$-32$$ $$0$$ $$0$$
3360.2.j.f $32$ $26.830$ None $$0$$ $$32$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3360, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3360, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(840, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1120, [\chi])$$$$^{\oplus 2}$$