Properties

 Label 177.3.g Level $177$ Weight $3$ Character orbit 177.g Rep. character $\chi_{177}(10,\cdot)$ Character field $\Q(\zeta_{58})$ Dimension $560$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$177 = 3 \cdot 59$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 177.g (of order $$58$$ and degree $$28$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$59$$ Character field: $$\Q(\zeta_{58})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(177, [\chi])$$.

Total New Old
Modular forms 1176 560 616
Cusp forms 1064 560 504
Eisenstein series 112 0 112

Trace form

 $$560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10})$$ $$560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(177, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
177.3.g.a $$560$$ $$4.823$$ None $$0$$ $$0$$ $$0$$ $$8$$

Decomposition of $$S_{3}^{\mathrm{old}}(177, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(177, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(59, [\chi])$$$$^{\oplus 2}$$