# Properties

 Label 882.3.s Level $882$ Weight $3$ Character orbit 882.s Rep. character $\chi_{882}(557,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $9$ Sturm bound $504$ Trace bound $25$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 882.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$504$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(882, [\chi])$$.

Total New Old
Modular forms 736 56 680
Cusp forms 608 56 552
Eisenstein series 128 0 128

## Trace form

 $$56 q + 56 q^{4} + O(q^{10})$$ $$56 q + 56 q^{4} - 16 q^{10} - 56 q^{13} - 112 q^{16} + 20 q^{19} + 252 q^{25} + 100 q^{31} - 32 q^{34} - 196 q^{37} + 32 q^{40} - 280 q^{43} + 224 q^{46} - 56 q^{52} - 176 q^{55} - 224 q^{58} + 64 q^{61} - 448 q^{64} + 588 q^{67} - 60 q^{73} + 80 q^{76} - 364 q^{79} - 96 q^{82} - 448 q^{85} - 192 q^{94} - 480 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(882, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.3.s.a $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots$$
882.3.s.b $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots$$
882.3.s.c $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots$$
882.3.s.d $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+2\beta _{3}q^{8}+\cdots$$
882.3.s.e $8$ $24.033$ 8.0.$$\cdots$$.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{6})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$$
882.3.s.f $8$ $24.033$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{6}q^{2}+2\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+\cdots$$
882.3.s.g $8$ $24.033$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{6}q^{2}+2\zeta_{24}^{2}q^{4}-2\zeta_{24}q^{5}+\cdots$$
882.3.s.h $8$ $24.033$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+2\beta _{1}q^{4}-\beta _{2}q^{5}+(-2\beta _{4}+\cdots)q^{8}+\cdots$$
882.3.s.i $8$ $24.033$ 8.0.$$\cdots$$.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{6})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(882, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(882, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$