Properties

 Label 1620.3.o Level $1620$ Weight $3$ Character orbit 1620.o Rep. character $\chi_{1620}(701,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $7$ Sturm bound $972$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1620 = 2^{2} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1620.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$7$$ Sturm bound: $$972$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

Dimensions

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

Total New Old
Modular forms 1368 64 1304
Cusp forms 1224 64 1160
Eisenstein series 144 0 144

Trace form

 $$64 q - 10 q^{7} + O(q^{10})$$ $$64 q - 10 q^{7} + 50 q^{13} + 92 q^{19} + 160 q^{25} + 80 q^{31} - 220 q^{37} - 280 q^{43} - 402 q^{49} + 98 q^{61} + 158 q^{67} - 76 q^{73} + 182 q^{79} - 60 q^{85} - 764 q^{91} - 310 q^{97} + O(q^{100})$$

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.o.a $4$ $44.142$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+(\beta _{1}-\beta _{3})q^{5}+(-8+8\beta _{2})q^{7}-9\beta _{1}q^{11}+\cdots$$
1620.3.o.b $4$ $44.142$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{1}+\beta _{3})q^{5}+(-2+2\beta _{2})q^{7}+\cdots$$
1620.3.o.c $4$ $44.142$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{1}q^{5}+4\beta _{2}q^{7}+(-3\beta _{1}+3\beta _{3})q^{11}+\cdots$$
1620.3.o.d $4$ $44.142$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$14$$ $$q+(\beta _{1}-\beta _{3})q^{5}+(7-7\beta _{2})q^{7}+6\beta _{1}q^{11}+\cdots$$
1620.3.o.e $8$ $44.142$ 8.0.12960000.1 None $$0$$ $$0$$ $$0$$ $$-20$$ $$q+(-\beta _{1}+\beta _{4})q^{5}+(-5+5\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots$$
1620.3.o.f $8$ $44.142$ 8.0.3317760000.8 None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{1}q^{5}+(4-4\beta _{2}-\beta _{7})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots$$
1620.3.o.g $32$ $44.142$ None $$0$$ $$0$$ $$0$$ $$-8$$

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

$$S_{3}^{\mathrm{old}}(1620, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 18}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(324, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(405, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(810, [\chi])$$$$^{\oplus 2}$$