# Properties

 Label 2160.2.q Level $2160$ Weight $2$ Character orbit 2160.q Rep. character $\chi_{2160}(721,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $48$ Newform subspaces $12$ Sturm bound $864$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2160.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$864$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2160, [\chi])$$.

Total New Old
Modular forms 936 48 888
Cusp forms 792 48 744
Eisenstein series 144 0 144

## Trace form

 $$48 q + O(q^{10})$$ $$48 q - 8 q^{17} - 12 q^{23} - 24 q^{25} + 4 q^{29} - 12 q^{31} - 24 q^{35} - 4 q^{41} - 12 q^{43} - 20 q^{47} - 24 q^{49} + 12 q^{59} + 24 q^{71} + 24 q^{73} + 16 q^{77} + 56 q^{83} + 24 q^{89} + 24 q^{91} - 16 q^{95} - 12 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2160, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2160.2.q.a $2$ $17.248$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-3$$ $$q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2160.2.q.b $2$ $17.248$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-1$$ $$q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
2160.2.q.c $2$ $17.248$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-3q^{17}-5q^{19}+\cdots$$
2160.2.q.d $2$ $17.248$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
2160.2.q.e $2$ $17.248$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+4\zeta_{6}q^{13}+\cdots$$
2160.2.q.f $4$ $17.248$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$-2$$ $$1$$ $$q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{3})q^{11}+\cdots$$
2160.2.q.g $4$ $17.248$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+(-1+\beta _{1})q^{5}+(\beta _{1}-\beta _{2})q^{7}+2q^{17}+\cdots$$
2160.2.q.h $4$ $17.248$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$4$$ $$q-\zeta_{12}q^{5}+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}+\cdots$$
2160.2.q.i $6$ $17.248$ 6.0.954288.1 None $$0$$ $$0$$ $$-3$$ $$3$$ $$q+(-1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots$$
2160.2.q.j $6$ $17.248$ 6.0.954288.1 None $$0$$ $$0$$ $$3$$ $$-5$$ $$q+(1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$$
2160.2.q.k $6$ $17.248$ 6.0.954288.1 None $$0$$ $$0$$ $$3$$ $$5$$ $$q+(1-\beta _{3})q^{5}+(2\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$$
2160.2.q.l $8$ $17.248$ 8.0.856615824.2 None $$0$$ $$0$$ $$4$$ $$-1$$ $$q+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+(\beta _{3}-\beta _{7})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2160, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2160, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1080, [\chi])$$$$^{\oplus 2}$$