# Properties

 Label 882.4.g Level $882$ Weight $4$ Character orbit 882.g Rep. character $\chi_{882}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $100$ Newform subspaces $37$ Sturm bound $672$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$37$$ Sturm bound: $$672$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(882, [\chi])$$.

Total New Old
Modular forms 1072 100 972
Cusp forms 944 100 844
Eisenstein series 128 0 128

## Trace form

 $$100q - 200q^{4} + 18q^{5} + O(q^{10})$$ $$100q - 200q^{4} + 18q^{5} - 8q^{10} + 2q^{11} + 192q^{13} - 800q^{16} + 150q^{17} - 46q^{19} - 144q^{20} - 400q^{22} - 350q^{23} - 1460q^{25} + 120q^{26} + 784q^{29} + 138q^{31} + 512q^{34} - 874q^{37} + 192q^{38} - 32q^{40} - 2016q^{41} - 896q^{43} + 8q^{44} - 136q^{46} - 102q^{47} + 736q^{50} - 384q^{52} + 2546q^{53} + 1916q^{55} + 552q^{58} - 90q^{59} + 294q^{61} - 3744q^{62} + 6400q^{64} - 2124q^{65} - 310q^{67} + 600q^{68} + 2688q^{71} - 1142q^{73} - 440q^{74} + 368q^{76} + 730q^{79} + 288q^{80} - 1200q^{82} - 2568q^{83} + 9476q^{85} + 1296q^{86} + 800q^{88} + 2754q^{89} + 2800q^{92} + 216q^{94} + 3122q^{95} + 160q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(882, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
882.4.g.a $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-22$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots$$
882.4.g.b $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-14$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots$$
882.4.g.c $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-8$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots$$
882.4.g.d $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-7$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots$$
882.4.g.e $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-6$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$$
882.4.g.f $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-6$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$$
882.4.g.g $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$6$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$$
882.4.g.h $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$6$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$$
882.4.g.i $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$6$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$$
882.4.g.j $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$8$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots$$
882.4.g.k $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$14$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots$$
882.4.g.l $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$15$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots$$
882.4.g.m $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$22$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots$$
882.4.g.n $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-22$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots$$
882.4.g.o $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-18$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots$$
882.4.g.p $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-12$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots$$
882.4.g.q $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-6$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$$
882.4.g.r $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$$
882.4.g.s $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$$
882.4.g.t $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$6$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$$
882.4.g.u $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$9$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots$$
882.4.g.v $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$12$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots$$
882.4.g.w $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$18$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots$$
882.4.g.x $$2$$ $$52.040$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$22$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots$$
882.4.g.y $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$-12$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.z $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{193})$$ None $$-4$$ $$0$$ $$-7$$ $$0$$ $$q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.ba $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots$$
882.4.g.bb $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{58})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$$
882.4.g.bc $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots$$
882.4.g.bd $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$12$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.be $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$4$$ $$0$$ $$-12$$ $$0$$ $$q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.bf $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{1345})$$ None $$4$$ $$0$$ $$-5$$ $$0$$ $$q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.bg $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots$$
882.4.g.bh $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{58})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots$$
882.4.g.bi $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{22})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots$$
882.4.g.bj $$4$$ $$52.040$$ $$\Q(\sqrt{-3}, \sqrt{193})$$ None $$4$$ $$0$$ $$7$$ $$0$$ $$q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
882.4.g.bk $$4$$ $$52.040$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$4$$ $$0$$ $$12$$ $$0$$ $$q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(882, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(882, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$