# Properties

 Label 810.3.j Level $810$ Weight $3$ Character orbit 810.j Rep. character $\chi_{810}(269,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $8$ Sturm bound $486$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$810 = 2 \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 810.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$486$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(810, [\chi])$$.

Total New Old
Modular forms 696 96 600
Cusp forms 600 96 504
Eisenstein series 96 0 96

## Trace form

 $$96 q - 96 q^{4} + O(q^{10})$$ $$96 q - 96 q^{4} - 192 q^{16} + 12 q^{25} + 120 q^{31} + 48 q^{46} + 288 q^{49} + 384 q^{55} - 96 q^{61} + 768 q^{64} - 240 q^{70} - 624 q^{79} - 24 q^{85} - 336 q^{91} + 168 q^{94} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(810, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
810.3.j.a $8$ $22.071$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{2}-2\beta _{4}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$$
810.3.j.b $8$ $22.071$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots$$
810.3.j.c $8$ $22.071$ 8.0.$$\cdots$$.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{6})q^{2}+(-2+2\beta _{1})q^{4}+\cdots$$
810.3.j.d $8$ $22.071$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots$$
810.3.j.e $8$ $22.071$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots$$
810.3.j.f $8$ $22.071$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$12$$ $$0$$ $$q+(\beta _{1}-\beta _{5})q^{2}-2\beta _{4}q^{4}+(\beta _{3}+3\beta _{4}+\cdots)q^{5}+\cdots$$
810.3.j.g $24$ $22.071$ None $$0$$ $$0$$ $$0$$ $$-24$$
810.3.j.h $24$ $22.071$ None $$0$$ $$0$$ $$0$$ $$24$$

## Decomposition of $$S_{3}^{\mathrm{old}}(810, [\chi])$$ into lower level spaces

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