# Properties

 Label 819.2.et Level $819$ Weight $2$ Character orbit 819.et Rep. character $\chi_{819}(136,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $180$ Newform subspaces $5$ Sturm bound $224$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$819 = 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 819.et (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$224$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(819, [\chi])$$.

Total New Old
Modular forms 480 196 284
Cusp forms 416 180 236
Eisenstein series 64 16 48

## Trace form

 $$180q + 2q^{2} + 6q^{5} + 2q^{7} + 4q^{8} + O(q^{10})$$ $$180q + 2q^{2} + 6q^{5} + 2q^{7} + 4q^{8} - 6q^{10} + 14q^{11} - 4q^{14} - 172q^{16} + 12q^{17} - 2q^{19} - 36q^{20} - 8q^{22} + 36q^{26} + 26q^{28} - 8q^{29} - 8q^{31} + 30q^{32} - 12q^{34} + 28q^{35} + 34q^{37} - 72q^{40} - 18q^{41} - 24q^{43} - 50q^{44} - 32q^{46} + 6q^{47} + 38q^{49} + 30q^{50} + 62q^{52} + 4q^{53} - 42q^{55} + 18q^{56} + 66q^{58} + 54q^{59} + 30q^{61} + 36q^{62} + 60q^{65} - 42q^{67} + 56q^{70} + 6q^{71} - 52q^{73} - 92q^{74} + 100q^{76} + 20q^{79} - 234q^{80} + 42q^{82} - 18q^{83} - 14q^{85} - 6q^{86} - 6q^{88} - 48q^{89} - 38q^{91} + 20q^{92} - 42q^{94} - 10q^{97} + 92q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(819, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
819.2.et.a $$4$$ $$6.540$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-8$$ $$q+2\zeta_{12}^{3}q^{4}+(-1-2\zeta_{12}^{2})q^{7}+(-4\zeta_{12}+\cdots)q^{13}+\cdots$$
819.2.et.b $$28$$ $$6.540$$ None $$2$$ $$0$$ $$6$$ $$-6$$
819.2.et.c $$36$$ $$6.540$$ None $$0$$ $$0$$ $$0$$ $$6$$
819.2.et.d $$40$$ $$6.540$$ None $$0$$ $$0$$ $$0$$ $$-2$$
819.2.et.e $$72$$ $$6.540$$ None $$0$$ $$0$$ $$0$$ $$12$$

## Decomposition of $$S_{2}^{\mathrm{old}}(819, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(819, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$