# Properties

 Label 77.2.e Level $77$ Weight $2$ Character orbit 77.e Rep. character $\chi_{77}(23,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $2$ Sturm bound $16$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$77 = 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 77.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(77, [\chi])$$.

Total New Old
Modular forms 20 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

## Trace form

 $$12 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + O(q^{10})$$ $$12 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 6 q^{10} + 6 q^{12} - 16 q^{13} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 2 q^{18} + 2 q^{19} + 40 q^{20} - 2 q^{21} - 12 q^{23} - 8 q^{24} - 6 q^{25} - 10 q^{26} + 16 q^{27} + 16 q^{28} - 24 q^{29} + 4 q^{30} - 6 q^{31} + 12 q^{32} - 4 q^{33} - 32 q^{34} - 6 q^{35} - 12 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 8 q^{41} - 20 q^{42} + 4 q^{43} + 4 q^{44} + 6 q^{45} + 34 q^{46} + 6 q^{47} - 16 q^{48} - 24 q^{49} + 24 q^{50} + 16 q^{51} - 2 q^{52} - 26 q^{53} + 26 q^{54} + 16 q^{55} + 6 q^{56} + 40 q^{57} - 2 q^{58} - 8 q^{59} - 12 q^{60} + 12 q^{61} + 20 q^{62} + 18 q^{63} - 20 q^{64} - 30 q^{65} + 2 q^{66} + 16 q^{67} + 16 q^{68} + 36 q^{69} + 18 q^{70} - 4 q^{71} - 22 q^{72} + 14 q^{73} - 40 q^{74} - 34 q^{75} - 96 q^{76} - 2 q^{77} + 18 q^{80} + 2 q^{81} - 38 q^{82} - 52 q^{83} + 12 q^{84} - 32 q^{85} + 30 q^{86} - 6 q^{87} - 12 q^{88} + 14 q^{89} - 52 q^{90} - 6 q^{91} + 44 q^{92} + 20 q^{93} + 10 q^{94} + 8 q^{95} - 30 q^{96} + 108 q^{97} - 30 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(77, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
77.2.e.a $6$ $0.615$ $$\Q(\zeta_{18})$$ None $$0$$ $$-3$$ $$-6$$ $$0$$ $$q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$$
77.2.e.b $6$ $0.615$ 6.0.1783323.2 None $$0$$ $$1$$ $$2$$ $$2$$ $$q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$