# Properties

 Label 819.2.fm Level $819$ Weight $2$ Character orbit 819.fm Rep. character $\chi_{819}(370,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $176$ Newform subspaces $8$ Sturm bound $224$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$819 = 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 819.fm (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$8$$ Sturm bound: $$224$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 480 192 288
Cusp forms 416 176 240
Eisenstein series 64 16 48

## Trace form

 $$176q + 8q^{2} - 12q^{4} - 4q^{7} + 16q^{8} + O(q^{10})$$ $$176q + 8q^{2} - 12q^{4} - 4q^{7} + 16q^{8} + 20q^{11} - 16q^{14} + 60q^{16} + 4q^{22} + 12q^{23} - 8q^{28} + 4q^{29} + 36q^{32} + 28q^{35} - 4q^{37} - 72q^{43} - 8q^{44} - 92q^{46} - 36q^{49} - 132q^{50} + 40q^{53} + 120q^{56} - 48q^{58} - 36q^{65} + 40q^{67} + 80q^{70} - 60q^{71} + 40q^{74} - 16q^{79} - 44q^{85} + 96q^{86} + 204q^{88} - 12q^{91} + 56q^{92} - 12q^{95} - 4q^{98} + O(q^{100})$$

## 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.fm.a $$4$$ $$6.540$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
819.2.fm.b $$4$$ $$6.540$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$2$$ $$-2$$ $$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
819.2.fm.c $$4$$ $$6.540$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{12}q^{4}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+(3\zeta_{12}+\cdots)q^{13}+\cdots$$
819.2.fm.d $$4$$ $$6.540$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$10$$ $$q-2\zeta_{12}q^{4}+(2+\zeta_{12}^{2})q^{7}+(-3\zeta_{12}+\cdots)q^{13}+\cdots$$
819.2.fm.e $$32$$ $$6.540$$ None $$2$$ $$0$$ $$-2$$ $$2$$
819.2.fm.f $$32$$ $$6.540$$ None $$2$$ $$0$$ $$2$$ $$-2$$
819.2.fm.g $$32$$ $$6.540$$ None $$8$$ $$0$$ $$0$$ $$0$$
819.2.fm.h $$64$$ $$6.540$$ None $$0$$ $$0$$ $$0$$ $$-12$$

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

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