# Properties

 Label 77.2.b Level $77$ Weight $2$ Character orbit 77.b Rep. character $\chi_{77}(76,\cdot)$ Character field $\Q$ Dimension $6$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q$$ 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 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6 q - 10 q^{4} - 2 q^{9} + O(q^{10})$$ $$6 q - 10 q^{4} - 2 q^{9} - 8 q^{11} - 2 q^{14} + 20 q^{15} + 6 q^{16} + 22 q^{22} - 28 q^{23} + 10 q^{25} - 30 q^{36} - 16 q^{37} + 20 q^{42} - 20 q^{44} - 22 q^{49} + 20 q^{53} + 66 q^{56} + 48 q^{58} - 58 q^{64} + 36 q^{67} - 20 q^{70} + 4 q^{71} + 2 q^{77} - 80 q^{78} - 26 q^{81} - 4 q^{86} - 26 q^{88} - 40 q^{91} + 80 q^{92} + 60 q^{93} + 36 q^{99} + O(q^{100})$$

## 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.b.a $2$ $0.615$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots$$
77.2.b.b $4$ $0.615$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$$