# Properties

 Label 69.2.g Level $69$ Weight $2$ Character orbit 69.g Rep. character $\chi_{69}(5,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $60$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$69 = 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 69.g (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(69, [\chi])$$.

Total New Old
Modular forms 100 100 0
Cusp forms 60 60 0
Eisenstein series 40 40 0

## Trace form

 $$60q - 11q^{3} - 10q^{4} - 14q^{6} - 22q^{7} - 11q^{9} + O(q^{10})$$ $$60q - 11q^{3} - 10q^{4} - 14q^{6} - 22q^{7} - 11q^{9} - 22q^{10} + 4q^{12} - 22q^{13} - 46q^{16} + 12q^{18} - 22q^{19} + 22q^{21} + 50q^{24} + 8q^{25} + 10q^{27} - 22q^{28} + 33q^{30} - 22q^{31} + 22q^{36} + 22q^{37} + 13q^{39} + 132q^{40} - 11q^{42} + 22q^{43} + 66q^{46} - 58q^{48} + 68q^{49} - 11q^{51} + 94q^{52} - 33q^{54} - 44q^{57} - 8q^{58} - 121q^{60} - 66q^{61} - 66q^{63} - 20q^{64} - 66q^{66} - 44q^{67} - 66q^{69} - 132q^{70} - 101q^{72} - 44q^{73} - 44q^{75} - 110q^{76} + 84q^{78} - 66q^{79} + 77q^{81} - 132q^{82} + 77q^{84} - 44q^{85} + 73q^{87} + 66q^{88} + 176q^{90} + 116q^{93} + 100q^{94} + 85q^{96} + 44q^{97} + 121q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(69, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
69.2.g.a $$60$$ $$0.551$$ None $$0$$ $$-11$$ $$0$$ $$-22$$