# Properties

 Label 242.2.c Level $242$ Weight $2$ Character orbit 242.c Rep. character $\chi_{242}(3,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $36$ Newform subspaces $7$ Sturm bound $66$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$242 = 2 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 242.c (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$7$$ Sturm bound: $$66$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 180 36 144
Cusp forms 84 36 48
Eisenstein series 96 0 96

## Trace form

 $$36q + q^{2} + 6q^{3} - 9q^{4} + 8q^{5} - q^{6} - 2q^{7} + q^{8} - 15q^{9} + O(q^{10})$$ $$36q + q^{2} + 6q^{3} - 9q^{4} + 8q^{5} - q^{6} - 2q^{7} + q^{8} - 15q^{9} - 4q^{10} - 14q^{12} + 4q^{13} - 2q^{14} - 2q^{15} - 9q^{16} - 2q^{17} + 8q^{18} + 5q^{19} + 8q^{20} + 12q^{21} - 12q^{23} - q^{24} - 13q^{25} - 4q^{26} + 3q^{27} - 2q^{28} - 10q^{29} - 6q^{30} + 10q^{31} - 4q^{32} - 18q^{34} - 12q^{35} + 28q^{37} - 8q^{38} + 6q^{39} - 4q^{40} + 2q^{41} + 6q^{42} - 6q^{43} - 12q^{45} + 4q^{46} + 16q^{47} + 6q^{48} - 5q^{49} + 11q^{50} + 7q^{51} - 6q^{52} + 10q^{53} + 8q^{56} - 5q^{57} - 4q^{58} + q^{59} + 8q^{60} - 8q^{61} + 2q^{62} - 16q^{63} - 9q^{64} - 16q^{65} - 94q^{67} - 2q^{68} + 2q^{69} + 16q^{70} + 4q^{71} - 7q^{72} + 14q^{73} + 18q^{74} + 31q^{75} + 10q^{76} - 16q^{78} + 30q^{79} - 2q^{80} + 19q^{82} + 19q^{83} - 8q^{84} - 2q^{85} - 11q^{86} + 20q^{87} - 54q^{89} - 12q^{90} - 52q^{91} - 2q^{92} - 62q^{93} - 12q^{94} + 10q^{95} + 4q^{96} - 57q^{97} + 12q^{98} + O(q^{100})$$

## 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.c.a $$4$$ $$1.932$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$4$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
242.2.c.b $$4$$ $$1.932$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$2$$ $$3$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
242.2.c.c $$4$$ $$1.932$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-4$$ $$-6$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots$$
242.2.c.d $$4$$ $$1.932$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$4$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$$
242.2.c.e $$4$$ $$1.932$$ $$\Q(\zeta_{10})$$ None $$1$$ $$2$$ $$3$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-2\zeta_{10}^{2}q^{3}+\cdots$$
242.2.c.f $$8$$ $$1.932$$ 8.0.324000000.3 None $$-2$$ $$2$$ $$0$$ $$-6$$ $$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$$
242.2.c.g $$8$$ $$1.932$$ 8.0.324000000.3 None $$2$$ $$2$$ $$0$$ $$6$$ $$q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(242, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$