# Properties

 Label 77.2.l Level $77$ Weight $2$ Character orbit 77.l Rep. character $\chi_{77}(6,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $24$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$77 = 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 77.l (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

## Trace form

 $$24q - 10q^{2} - 10q^{7} + 2q^{9} + O(q^{10})$$ $$24q - 10q^{2} - 10q^{7} + 2q^{9} - 2q^{11} - 13q^{14} - 6q^{16} - 35q^{18} + 28q^{22} + 8q^{23} - 40q^{25} + 25q^{28} + 10q^{29} - 40q^{30} + 40q^{35} + 50q^{36} - 14q^{37} + 30q^{39} + 50q^{42} + 15q^{44} + 5q^{46} + 22q^{49} - 60q^{50} - 10q^{51} + 30q^{53} - 46q^{56} - 90q^{57} + 17q^{58} + 120q^{60} - 20q^{63} - 72q^{64} + 4q^{67} - 104q^{71} - 45q^{72} + 90q^{74} - 12q^{77} - 20q^{78} + 10q^{79} - 34q^{81} - 70q^{84} + 80q^{85} + 29q^{86} - 94q^{88} - 30q^{91} + 45q^{92} - 40q^{93} - 60q^{95} + 84q^{99} + O(q^{100})$$

## 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.l.a $$8$$ $$0.615$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots$$
77.2.l.b $$16$$ $$0.615$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-10$$ $$0$$ $$0$$ $$-10$$ $$q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$$