# Properties

 Label 882.2.f Level $882$ Weight $2$ Character orbit 882.f Rep. character $\chi_{882}(295,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $82$ Newform subspaces $19$ Sturm bound $336$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.f (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$19$$ Sturm bound: $$336$$ Trace bound: $$9$$ 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 368 82 286
Cusp forms 304 82 222
Eisenstein series 64 0 64

## Trace form

 $$82 q - q^{2} - 3 q^{3} - 41 q^{4} + 4 q^{5} - 5 q^{6} + 2 q^{8} - 9 q^{9} + O(q^{10})$$ $$82 q - q^{2} - 3 q^{3} - 41 q^{4} + 4 q^{5} - 5 q^{6} + 2 q^{8} - 9 q^{9} - 5 q^{11} + 2 q^{13} + 4 q^{15} - 41 q^{16} + 2 q^{17} + 10 q^{18} - 10 q^{19} + 4 q^{20} + 3 q^{22} - 14 q^{23} + q^{24} - 35 q^{25} - 4 q^{26} + 36 q^{27} + 6 q^{29} - 12 q^{30} + 8 q^{31} - q^{32} - 5 q^{33} + 3 q^{34} + 3 q^{36} - 16 q^{37} + 13 q^{38} - 28 q^{39} + 27 q^{41} + 5 q^{43} + 10 q^{44} + 40 q^{45} + 12 q^{46} - 6 q^{47} + 3 q^{48} - 19 q^{50} + 29 q^{51} + 2 q^{52} - 8 q^{53} - 11 q^{54} - 24 q^{55} - 9 q^{57} + 6 q^{58} - 11 q^{59} - 8 q^{60} + 8 q^{61} - 16 q^{62} + 82 q^{64} - 44 q^{65} - 32 q^{66} + 23 q^{67} - q^{68} - 32 q^{69} - 16 q^{71} - 5 q^{72} - 34 q^{73} - 8 q^{74} - 7 q^{75} + 5 q^{76} - 38 q^{78} - 4 q^{79} - 8 q^{80} + 35 q^{81} + 18 q^{82} + 56 q^{83} - 24 q^{85} - 7 q^{86} - 34 q^{87} + 3 q^{88} + 12 q^{89} + 52 q^{90} - 14 q^{92} + 16 q^{93} - 6 q^{94} + 36 q^{95} + 4 q^{96} - q^{97} - 50 q^{99} + O(q^{100})$$

## 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.f.a $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-3$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.b $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.c $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.d $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.e $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$3$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.f $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$2$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.g $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$3$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.h $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-3$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.i $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-3$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.f.j $4$ $7.043$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$-4$$ $$2$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
882.2.f.k $4$ $7.043$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$1$$ $$3$$ $$0$$ $$q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
882.2.f.l $6$ $7.043$ 6.0.309123.1 None $$-3$$ $$-2$$ $$-5$$ $$0$$ $$q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$$
882.2.f.m $6$ $7.043$ 6.0.309123.1 None $$-3$$ $$2$$ $$5$$ $$0$$ $$q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots$$
882.2.f.n $6$ $7.043$ 6.0.309123.1 None $$3$$ $$-4$$ $$1$$ $$0$$ $$q+(1+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$$
882.2.f.o $6$ $7.043$ 6.0.309123.1 None $$3$$ $$4$$ $$-1$$ $$0$$ $$q+(1+\beta _{4})q^{2}+(1-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$$
882.2.f.p $8$ $7.043$ 8.0.3317760000.3 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{6})q^{3}+\cdots$$
882.2.f.q $8$ $7.043$ $$\Q(\zeta_{24})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}+(-1+\cdots)q^{4}+\cdots$$
882.2.f.r $8$ $7.043$ 8.0.$$\cdots$$.2 None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{4})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$$
882.2.f.s $8$ $7.043$ $$\Q(\zeta_{24})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(882, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$