# Properties

 Label 121.2.c Level $121$ Weight $2$ Character orbit 121.c Rep. character $\chi_{121}(3,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $20$ Newform subspaces $5$ Sturm bound $22$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$121 = 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 121.c (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$5$$ Sturm bound: $$22$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(121, [\chi])$$.

Total New Old
Modular forms 68 52 16
Cusp forms 20 20 0
Eisenstein series 48 32 16

## Trace form

 $$20q - q^{3} - q^{5} + 4q^{9} + O(q^{10})$$ $$20q - q^{3} - q^{5} + 4q^{9} - 24q^{12} - 4q^{14} - 5q^{15} + 6q^{16} - 8q^{20} - 28q^{23} + 12q^{25} + 14q^{26} - 7q^{27} - 5q^{31} - 8q^{34} + 6q^{36} - 7q^{37} - 12q^{38} + 16q^{42} + 16q^{45} - 8q^{47} + 19q^{49} - 12q^{53} + 48q^{56} - 18q^{58} - 11q^{59} + 14q^{60} + 10q^{64} + 12q^{67} - 19q^{69} - 4q^{70} - 15q^{71} + 12q^{75} + 80q^{78} + 22q^{80} + 19q^{81} - 22q^{82} - 24q^{86} + 12q^{89} + 20q^{91} - 10q^{92} + 17q^{93} + 23q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(121, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
121.2.c.a $$4$$ $$0.966$$ $$\Q(\zeta_{10})$$ None $$-2$$ $$1$$ $$-1$$ $$-2$$ $$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$$
121.2.c.b $$4$$ $$0.966$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-2$$ $$-1$$ $$2$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
121.2.c.c $$4$$ $$0.966$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$1$$ $$3$$ $$0$$ $$q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots$$
121.2.c.d $$4$$ $$0.966$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-2$$ $$-1$$ $$-2$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots$$
121.2.c.e $$4$$ $$0.966$$ $$\Q(\zeta_{10})$$ None $$2$$ $$1$$ $$-1$$ $$2$$ $$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$$