# Properties

 Label 882.3.c Level $882$ Weight $3$ Character orbit 882.c Rep. character $\chi_{882}(685,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $7$ Sturm bound $504$ Trace bound $23$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 882.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$504$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$5$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(882, [\chi])$$.

Total New Old
Modular forms 368 32 336
Cusp forms 304 32 272
Eisenstein series 64 0 64

## Trace form

 $$32 q + 64 q^{4} + O(q^{10})$$ $$32 q + 64 q^{4} - 36 q^{11} + 128 q^{16} - 40 q^{22} - 4 q^{23} - 36 q^{25} + 176 q^{29} + 20 q^{37} + 32 q^{43} - 72 q^{44} - 72 q^{46} + 88 q^{50} - 204 q^{53} + 104 q^{58} + 256 q^{64} + 480 q^{65} - 292 q^{67} - 64 q^{71} + 72 q^{74} - 228 q^{79} - 132 q^{85} - 320 q^{86} - 80 q^{88} - 8 q^{92} - 212 q^{95} + O(q^{100})$$

## 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.c.a $$4$$ $$24.033$$ 4.0.2048.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+4\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots$$
882.3.c.b $$4$$ $$24.033$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-2\beta _{3})q^{5}-2\beta _{1}q^{8}+\cdots$$
882.3.c.c $$4$$ $$24.033$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2q^{4}+2\beta _{3}q^{5}-2\beta _{1}q^{8}+\cdots$$
882.3.c.d $$4$$ $$24.033$$ 4.0.2048.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots$$
882.3.c.e $$4$$ $$24.033$$ 4.0.2048.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots$$
882.3.c.f $$4$$ $$24.033$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+2q^{4}+(\beta _{2}+2\beta _{3})q^{5}+2\beta _{1}q^{8}+\cdots$$
882.3.c.g $$8$$ $$24.033$$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+2q^{4}+(-\beta _{2}-\beta _{4})q^{5}+2\beta _{1}q^{8}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(882, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$