# Properties

 Label 882.2.h Level $882$ Weight $2$ Character orbit 882.h Rep. character $\chi_{882}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $20$ 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.h (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$20$$ 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 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

## Trace form

 $$80 q - 40 q^{4} - 8 q^{5} + 4 q^{6} + 6 q^{9} + O(q^{10})$$ $$80 q - 40 q^{4} - 8 q^{5} + 4 q^{6} + 6 q^{9} + 16 q^{11} - 2 q^{13} - 14 q^{15} - 40 q^{16} + 14 q^{17} - 20 q^{18} + 4 q^{19} + 4 q^{20} + 4 q^{23} - 2 q^{24} + 80 q^{25} + 16 q^{26} + 18 q^{29} - 18 q^{30} - 2 q^{31} - 2 q^{33} + 12 q^{36} - 2 q^{37} - 24 q^{38} + 2 q^{39} + 6 q^{41} - 2 q^{43} - 8 q^{44} + 28 q^{45} + 6 q^{46} + 6 q^{47} - 4 q^{51} + 4 q^{52} - 32 q^{53} - 2 q^{54} + 12 q^{55} - 30 q^{57} + 12 q^{58} + 22 q^{59} - 14 q^{60} - 8 q^{61} - 44 q^{62} + 80 q^{64} - 2 q^{65} - 8 q^{66} - 14 q^{67} - 28 q^{68} - 38 q^{69} - 76 q^{71} + 4 q^{72} + 28 q^{73} - 12 q^{74} + 74 q^{75} + 4 q^{76} - 56 q^{78} - 32 q^{79} + 4 q^{80} + 26 q^{81} - 16 q^{83} - 24 q^{85} + 40 q^{86} + 56 q^{87} + 36 q^{89} - 2 q^{90} - 2 q^{92} - 86 q^{93} - 12 q^{94} - 42 q^{95} - 2 q^{96} - 2 q^{97} + 34 q^{99} + O(q^{100})$$

## 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.h.a $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.b $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.c $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.d $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.e $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$6$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.f $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$6$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.g $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-4$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.h $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$4$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.i $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-6$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.j $2$ $7.043$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-6$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
882.2.h.k $4$ $7.043$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$-2$$ $$4$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$$
882.2.h.l $4$ $7.043$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$-4$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
882.2.h.m $4$ $7.043$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$-1$$ $$6$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$$
882.2.h.n $4$ $7.043$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$1$$ $$-6$$ $$0$$ $$q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
882.2.h.o $6$ $7.043$ 6.0.309123.1 None $$-3$$ $$-4$$ $$-10$$ $$0$$ $$q+(-1-\beta _{4})q^{2}+(\beta _{2}+\beta _{3}-\beta _{5})q^{3}+\cdots$$
882.2.h.p $6$ $7.043$ 6.0.309123.1 None $$3$$ $$-2$$ $$2$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$$
882.2.h.q $8$ $7.043$ $$\Q(\zeta_{24})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{24})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{6})q^{3}+\cdots$$
882.2.h.r $8$ $7.043$ 8.0.3317760000.3 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$$
882.2.h.s $8$ $7.043$ 8.0.$$\cdots$$.2 None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{4})q^{2}+(\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$$
882.2.h.t $8$ $7.043$ $$\Q(\zeta_{24})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1-\zeta_{24})q^{2}+(-\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+\cdots$$

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

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