# Properties

 Label 69.3.b Level $69$ Weight $3$ Character orbit 69.b Rep. character $\chi_{69}(47,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$69 = 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 69.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(69, [\chi])$$.

Total New Old
Modular forms 18 14 4
Cusp forms 14 14 0
Eisenstein series 4 0 4

## Trace form

 $$14q - 4q^{3} - 24q^{4} + 11q^{6} - 4q^{7} - 8q^{9} + O(q^{10})$$ $$14q - 4q^{3} - 24q^{4} + 11q^{6} - 4q^{7} - 8q^{9} - 8q^{10} + 19q^{12} - 14q^{15} + 72q^{16} - 31q^{18} + 8q^{19} - 2q^{21} - 84q^{22} - 44q^{24} + 38q^{25} + 62q^{27} + 76q^{28} + 62q^{30} - 144q^{31} + 90q^{33} - 68q^{34} + 3q^{36} + 48q^{37} - 78q^{39} + 120q^{40} - 76q^{42} - 48q^{43} - 18q^{45} - 317q^{48} - 30q^{49} + 18q^{51} - 6q^{52} + 312q^{54} + 232q^{55} + 76q^{57} + 66q^{58} - 36q^{60} - 140q^{61} - 206q^{63} - 346q^{64} + 398q^{66} + 204q^{67} + 80q^{70} + 384q^{72} - 224q^{73} - 80q^{75} + 100q^{76} - 341q^{78} - 344q^{79} - 232q^{81} - 62q^{82} - 330q^{84} + 480q^{85} + 86q^{87} + 436q^{88} - 514q^{90} - 172q^{91} + 62q^{93} + 514q^{94} + 609q^{96} - 24q^{97} + 234q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(69, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
69.3.b.a $$14$$ $$1.880$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$$