# Properties

 Label 177.2.d Level $177$ Weight $2$ Character orbit 177.d Rep. character $\chi_{177}(176,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $3$ Sturm bound $40$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$177 = 3 \cdot 59$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 177.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$177$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$40$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(177, [\chi])$$.

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

## Trace form

 $$18q - 2q^{3} + 12q^{4} - 10q^{9} + O(q^{10})$$ $$18q - 2q^{3} + 12q^{4} - 10q^{9} - 14q^{12} + 9q^{15} + 8q^{16} + 8q^{19} - 5q^{21} + 4q^{22} - 38q^{25} + 25q^{27} - 32q^{28} - 42q^{36} + q^{45} - 12q^{46} - 2q^{48} - 10q^{49} + 28q^{51} + 33q^{57} + 40q^{60} + 34q^{63} - 68q^{64} - 52q^{66} + 28q^{75} + 92q^{76} - 16q^{78} - 28q^{79} - 42q^{81} + 40q^{84} + 28q^{85} + 7q^{87} - 80q^{88} + 104q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(177, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
177.2.d.a $$6$$ $$1.413$$ 6.0.19298288.1 None $$-4$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}+\beta _{2}+\beta _{5})q^{2}-\beta _{1}q^{3}+\cdots$$
177.2.d.b $$6$$ $$1.413$$ 6.0.149721291.1 $$\Q(\sqrt{-59})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-2q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
177.2.d.c $$6$$ $$1.413$$ 6.0.19298288.1 None $$4$$ $$-1$$ $$0$$ $$0$$ $$q+(1-\beta _{1}-\beta _{2}-\beta _{5})q^{2}-\beta _{1}q^{3}+(2+\cdots)q^{4}+\cdots$$