# Properties

 Label 138.2.f Level $138$ Weight $2$ Character orbit 138.f Rep. character $\chi_{138}(5,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $80$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$138 = 2 \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 138.f (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(138, [\chi])$$.

Total New Old
Modular forms 280 80 200
Cusp forms 200 80 120
Eisenstein series 80 0 80

## Trace form

 $$80q + 4q^{3} + 8q^{4} + 4q^{6} + O(q^{10})$$ $$80q + 4q^{3} + 8q^{4} + 4q^{6} - 4q^{12} + 8q^{13} - 22q^{15} - 8q^{16} - 28q^{18} - 66q^{21} - 4q^{24} - 48q^{25} - 38q^{27} - 44q^{30} - 16q^{31} - 22q^{33} - 44q^{37} - 24q^{39} - 44q^{43} - 16q^{46} + 4q^{48} - 76q^{49} - 8q^{52} - 6q^{54} + 64q^{55} + 66q^{57} + 36q^{58} + 22q^{60} + 88q^{61} + 110q^{63} + 8q^{64} + 88q^{66} + 44q^{67} + 82q^{69} + 112q^{70} + 28q^{72} + 52q^{73} + 136q^{75} + 82q^{78} + 88q^{79} + 36q^{81} + 44q^{82} + 22q^{84} + 20q^{85} - 10q^{87} + 8q^{93} - 56q^{94} + 4q^{96} - 132q^{97} - 66q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(138, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
138.2.f.a $$80$$ $$1.102$$ None $$0$$ $$4$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(138, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(138, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 2}$$