# Properties

 Label 1620.2.i Level $1620$ Weight $2$ Character orbit 1620.i Rep. character $\chi_{1620}(541,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $14$ Sturm bound $648$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1620 = 2^{2} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1620.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$648$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1620, [\chi])$$.

Total New Old
Modular forms 720 32 688
Cusp forms 576 32 544
Eisenstein series 144 0 144

## Trace form

 $$32 q + 10 q^{7} + O(q^{10})$$ $$32 q + 10 q^{7} + 10 q^{13} - 44 q^{19} - 16 q^{25} - 20 q^{31} - 20 q^{37} - 8 q^{43} + 6 q^{49} + 10 q^{61} + 10 q^{67} - 20 q^{73} - 2 q^{79} - 12 q^{85} + 68 q^{91} + 22 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1620, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.2.i.a $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$$
1620.2.i.b $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$$
1620.2.i.c $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
1620.2.i.d $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
1620.2.i.e $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$4$$ $$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1620.2.i.f $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$4$$ $$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
1620.2.i.g $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$$
1620.2.i.h $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$$
1620.2.i.i $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$$
1620.2.i.j $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$1$$ $$q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
1620.2.i.k $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
1620.2.i.l $2$ $12.936$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
1620.2.i.m $4$ $12.936$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+(-1+\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots$$
1620.2.i.n $4$ $12.936$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$2$$ $$q+(1-\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\zeta_{12}^{2}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1620, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1620, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(324, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(405, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(810, [\chi])$$$$^{\oplus 2}$$