# Properties

 Label 882.2.g Level $882$ Weight $2$ Character orbit 882.g Rep. character $\chi_{882}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $13$ Sturm bound $336$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$13$$ Sturm bound: $$336$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(882, [\chi])$$.

Total New Old
Modular forms 400 32 368
Cusp forms 272 32 240
Eisenstein series 128 0 128

## Trace form

 $$32 q - 16 q^{4} - 4 q^{5} + O(q^{10})$$ $$32 q - 16 q^{4} - 4 q^{5} + 4 q^{10} - 12 q^{11} - 16 q^{16} + 4 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 4 q^{23} - 12 q^{25} - 4 q^{26} + 8 q^{29} - 12 q^{31} - 16 q^{34} + 8 q^{37} - 12 q^{38} + 4 q^{40} - 24 q^{43} - 12 q^{44} - 24 q^{46} + 12 q^{47} + 32 q^{50} - 12 q^{53} + 8 q^{55} - 20 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 32 q^{64} - 4 q^{65} + 24 q^{67} + 4 q^{68} - 8 q^{71} + 16 q^{73} - 4 q^{74} - 16 q^{76} + 60 q^{79} - 4 q^{80} - 32 q^{83} - 48 q^{85} - 16 q^{86} - 8 q^{88} - 8 q^{92} + 24 q^{94} + 4 q^{95} + 40 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(882, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.2.g.a $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots$$
882.2.g.b $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-3$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$$
882.2.g.c $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}-4q^{13}+\cdots$$
882.2.g.d $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}+4q^{13}+\cdots$$
882.2.g.e $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$3$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$$
882.2.g.f $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$4$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots$$
882.2.g.g $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-3$$ $$0$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$$
882.2.g.h $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$$
882.2.g.i $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}-q^{8}+\cdots$$
882.2.g.j $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$$
882.2.g.k $4$ $7.043$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+q^{8}+\cdots$$
882.2.g.l $4$ $7.043$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}-q^{8}+\cdots$$
882.2.g.m $4$ $7.043$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}-q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(882, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(882, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$