# Properties

 Label 722.2.c Level $722$ Weight $2$ Character orbit 722.c Rep. character $\chi_{722}(429,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $54$ Newform subspaces $14$ Sturm bound $190$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$190$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(722, [\chi])$$.

Total New Old
Modular forms 230 54 176
Cusp forms 150 54 96
Eisenstein series 80 0 80

## Trace form

 $$54q + q^{2} + q^{3} - 27q^{4} + 4q^{5} - q^{6} - 2q^{8} - 24q^{9} + O(q^{10})$$ $$54q + q^{2} + q^{3} - 27q^{4} + 4q^{5} - q^{6} - 2q^{8} - 24q^{9} + 2q^{10} - 2q^{11} - 2q^{12} + 6q^{13} + 6q^{14} - 14q^{15} - 27q^{16} - 4q^{17} - 20q^{18} - 8q^{20} + 10q^{21} - 7q^{22} - 2q^{23} - q^{24} - 27q^{25} - 4q^{26} + 10q^{27} - 2q^{29} + 28q^{30} + 8q^{31} + q^{32} - 11q^{33} + 6q^{34} - 8q^{35} - 24q^{36} + 8q^{37} - 16q^{39} + 2q^{40} + 19q^{41} + 24q^{42} + 18q^{43} + q^{44} - 36q^{45} - 16q^{46} + 22q^{47} + q^{48} + 18q^{49} - 22q^{50} - 6q^{51} + 6q^{52} + 2q^{53} + 11q^{54} + 22q^{55} - 12q^{56} - 4q^{58} - 9q^{59} - 14q^{60} - 12q^{61} - 8q^{62} + 32q^{63} + 54q^{64} - 8q^{65} - 13q^{66} - 11q^{67} + 8q^{68} + 40q^{69} - 12q^{70} - 22q^{71} + 10q^{72} + 27q^{73} + 22q^{74} + 66q^{75} + 52q^{77} - 2q^{78} - 12q^{79} + 4q^{80} - 31q^{81} + 5q^{82} - 26q^{83} - 20q^{84} + 12q^{85} + 16q^{86} - 56q^{87} + 14q^{88} + 6q^{89} + 8q^{90} - 4q^{91} - 2q^{92} - 28q^{94} + 2q^{96} - q^{97} - 7q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(722, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
722.2.c.a $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-2$$ $$-6$$ $$q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.b $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-8$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.c $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.d $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$4$$ $$6$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.e $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.f $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$4$$ $$6$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.g $$2$$ $$5.765$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-2$$ $$-6$$ $$q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.h $$4$$ $$5.765$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-2$$ $$2$$ $$5$$ $$-4$$ $$q+(-1-\beta _{3})q^{2}+2\beta _{1}q^{3}+\beta _{3}q^{4}+\cdots$$
722.2.c.i $$4$$ $$5.765$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$2$$ $$-2$$ $$5$$ $$-4$$ $$q+(1+\beta _{3})q^{2}-2\beta _{1}q^{3}+\beta _{3}q^{4}+(3+\cdots)q^{5}+\cdots$$
722.2.c.j $$4$$ $$5.765$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$0$$ $$-2$$ $$4$$ $$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
722.2.c.k $$6$$ $$5.765$$ $$\Q(\zeta_{18})$$ None $$-3$$ $$0$$ $$-6$$ $$12$$ $$q+(-1+\zeta_{18})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+\cdots$$
722.2.c.l $$6$$ $$5.765$$ $$\Q(\zeta_{18})$$ None $$3$$ $$0$$ $$-6$$ $$12$$ $$q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$$
722.2.c.m $$8$$ $$5.765$$ 8.0.324000000.2 None $$-4$$ $$-2$$ $$2$$ $$-4$$ $$q+(-1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$$
722.2.c.n $$8$$ $$5.765$$ 8.0.324000000.2 None $$4$$ $$2$$ $$2$$ $$-4$$ $$q+(1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(722, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(722, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(361, [\chi])$$$$^{\oplus 2}$$