# Properties

 Label 242.2.g Level $242$ Weight $2$ Character orbit 242.g Rep. character $\chi_{242}(5,\cdot)$ Character field $\Q(\zeta_{55})$ Dimension $440$ Newform subspaces $2$ Sturm bound $66$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$242 = 2 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 242.g (of order $$55$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{55})$$ Newform subspaces: $$2$$ Sturm bound: $$66$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(242, [\chi])$$.

Total New Old
Modular forms 1400 440 960
Cusp forms 1240 440 800
Eisenstein series 160 0 160

## Trace form

 $$440q + q^{2} + 2q^{3} + 11q^{4} + 4q^{5} - q^{6} - 2q^{7} + q^{8} - 120q^{9} + O(q^{10})$$ $$440q + q^{2} + 2q^{3} + 11q^{4} + 4q^{5} - q^{6} - 2q^{7} + q^{8} - 120q^{9} - 26q^{10} - 21q^{11} - 9q^{12} - 62q^{13} - 24q^{14} - 54q^{15} + 11q^{16} - 2q^{17} + 8q^{18} + 5q^{19} + 4q^{20} + 12q^{21} - 33q^{22} + 20q^{23} - q^{24} - 5q^{25} - 8q^{26} - 13q^{27} - 2q^{28} - 10q^{29} - 6q^{30} - 50q^{31} - 4q^{32} - 11q^{33} + 14q^{34} - 12q^{35} + 16q^{36} - 58q^{37} - 78q^{38} + 6q^{39} - 26q^{40} + 2q^{41} - 2q^{42} - 6q^{43} - 4q^{44} + 68q^{45} + 4q^{46} + 2q^{48} - 89q^{49} + 11q^{50} - 114q^{51} - 6q^{52} - 68q^{53} - 48q^{55} + 8q^{56} - 16q^{57} - 60q^{58} - 11q^{59} - 8q^{61} + 2q^{62} - 126q^{63} + 11q^{64} - 82q^{65} - 27q^{66} - 60q^{67} - 2q^{68} - 30q^{69} - 44q^{70} - 64q^{71} - 7q^{72} - 30q^{73} + 18q^{74} - 13q^{75} - 45q^{76} - 36q^{77} + 48q^{78} - 80q^{79} - 6q^{80} - 149q^{81} - 49q^{82} + 19q^{83} - 8q^{84} - 222q^{85} - 31q^{86} + 20q^{87} - 32q^{88} - 80q^{89} - 188q^{90} - 210q^{91} - 98q^{92} - 96q^{93} - 188q^{94} - 166q^{95} + 4q^{96} - 91q^{97} - 76q^{98} - 97q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(242, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
242.2.g.a $$200$$ $$1.932$$ None $$-5$$ $$10$$ $$-1$$ $$0$$
242.2.g.b $$240$$ $$1.932$$ None $$6$$ $$-8$$ $$5$$ $$-2$$

## Decomposition of $$S_{2}^{\mathrm{old}}(242, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(242, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$