# Properties

 Label 1620.3.t Level $1620$ Weight $3$ Character orbit 1620.t Rep. character $\chi_{1620}(269,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $6$ Sturm bound $972$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1620 = 2^{2} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1620.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$972$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1620, [\chi])$$.

Total New Old
Modular forms 1368 96 1272
Cusp forms 1224 96 1128
Eisenstein series 144 0 144

## Trace form

 $$96 q + O(q^{10})$$ $$96 q - 6 q^{25} - 60 q^{31} + 288 q^{49} - 12 q^{55} - 96 q^{61} - 588 q^{79} - 24 q^{85} + 168 q^{91} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1620, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.3.t.a $8$ $44.142$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(\beta _{2}-\beta _{7})q^{5}+\beta _{1}q^{7}+(-3\beta _{1}-2\beta _{4}+\cdots)q^{11}+\cdots$$
1620.3.t.b $8$ $44.142$ 8.0.12960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{5}-2\beta _{4}q^{7}+(\beta _{2}+2\beta _{5}+2\beta _{6}+\cdots)q^{11}+\cdots$$
1620.3.t.c $8$ $44.142$ 8.0.$$\cdots$$.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{5}+\beta _{6})q^{5}+\beta _{3}q^{7}-7\beta _{4}q^{11}+\cdots$$
1620.3.t.d $8$ $44.142$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(-\beta _{2}+\beta _{7})q^{5}+\beta _{1}q^{7}+(3\beta _{1}+2\beta _{4}+\cdots)q^{11}+\cdots$$
1620.3.t.e $16$ $44.142$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\beta _{14}q^{11}+\cdots$$
1620.3.t.f $48$ $44.142$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1620, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1620, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(405, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(810, [\chi])$$$$^{\oplus 2}$$