# Properties

 Label 882.2.z Level $882$ Weight $2$ Character orbit 882.z Rep. character $\chi_{882}(37,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $288$ Newform subspaces $8$ Sturm bound $336$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.z (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$8$$ Sturm bound: $$336$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 2112 288 1824
Cusp forms 1920 288 1632
Eisenstein series 192 0 192

## Trace form

 $$288q + 24q^{4} - 4q^{5} - 4q^{7} + O(q^{10})$$ $$288q + 24q^{4} - 4q^{5} - 4q^{7} + 4q^{10} - 18q^{11} + 8q^{14} + 24q^{16} - 10q^{17} - 6q^{19} - 6q^{20} + 14q^{22} + 46q^{23} + 28q^{25} - 18q^{26} - 4q^{28} + 22q^{29} - 12q^{31} - 16q^{34} - 22q^{35} + 44q^{37} + 16q^{38} - 24q^{40} + 56q^{41} + 32q^{43} + 24q^{44} + 76q^{46} + 68q^{47} - 84q^{49} - 8q^{50} - 14q^{52} + 134q^{53} - 34q^{55} + 24q^{56} - 84q^{58} + 50q^{59} - 136q^{61} + 36q^{62} - 48q^{64} - 12q^{67} + 32q^{68} - 14q^{70} + 34q^{71} - 26q^{73} - 14q^{74} - 16q^{76} - 70q^{77} - 8q^{79} + 10q^{80} + 80q^{83} + 32q^{85} - 50q^{86} - 14q^{88} + 84q^{89} + 66q^{91} - 8q^{92} + 10q^{94} + 116q^{95} + 12q^{97} + 52q^{98} + O(q^{100})$$

## 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.z.a $$24$$ $$7.043$$ None $$-2$$ $$0$$ $$-1$$ $$0$$
882.2.z.b $$24$$ $$7.043$$ None $$-2$$ $$0$$ $$0$$ $$0$$
882.2.z.c $$24$$ $$7.043$$ None $$2$$ $$0$$ $$-1$$ $$0$$
882.2.z.d $$24$$ $$7.043$$ None $$2$$ $$0$$ $$0$$ $$0$$
882.2.z.e $$36$$ $$7.043$$ None $$-3$$ $$0$$ $$0$$ $$-1$$
882.2.z.f $$36$$ $$7.043$$ None $$3$$ $$0$$ $$-2$$ $$-5$$
882.2.z.g $$60$$ $$7.043$$ None $$-5$$ $$0$$ $$-3$$ $$1$$
882.2.z.h $$60$$ $$7.043$$ None $$5$$ $$0$$ $$3$$ $$1$$

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

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