# Properties

 Label 882.3.b Level $882$ Weight $3$ Character orbit 882.b Rep. character $\chi_{882}(197,\cdot)$ Character field $\Q$ Dimension $26$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ 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 368 26 342
Cusp forms 304 26 278
Eisenstein series 64 0 64

## Trace form

 $$26 q - 52 q^{4} + O(q^{10})$$ $$26 q - 52 q^{4} - 20 q^{10} + 16 q^{13} + 104 q^{16} - 48 q^{19} + 48 q^{22} - 74 q^{25} - 104 q^{31} + 68 q^{34} + 36 q^{37} + 40 q^{40} - 264 q^{43} - 176 q^{46} - 32 q^{52} + 320 q^{55} - 76 q^{58} - 332 q^{61} - 208 q^{64} - 520 q^{67} + 128 q^{73} + 96 q^{76} + 576 q^{79} + 348 q^{82} - 332 q^{85} - 96 q^{88} - 144 q^{94} - 64 q^{97} + O(q^{100})$$

## 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.b.a $2$ $24.033$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots$$
882.3.b.b $2$ $24.033$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots$$
882.3.b.c $2$ $24.033$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots$$
882.3.b.d $2$ $24.033$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-2q^{4}+\beta q^{5}+2\beta q^{8}+2q^{10}+\cdots$$
882.3.b.e $2$ $24.033$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots$$
882.3.b.f $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{1}q^{8}+\cdots$$
882.3.b.g $4$ $24.033$ $$\Q(\sqrt{-2}, \sqrt{37})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots$$
882.3.b.h $4$ $24.033$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots$$
882.3.b.i $4$ $24.033$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}-2q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(882, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$