Properties

 Label 117.1.j Level $117$ Weight $1$ Character orbit 117.j Rep. character $\chi_{117}(73,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $14$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$117 = 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 117.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$14$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(117, [\chi])$$.

Total New Old
Modular forms 10 4 6
Cusp forms 2 2 0
Eisenstein series 8 2 6

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

Trace form

 $$2 q - 2 q^{7} + O(q^{10})$$ $$2 q - 2 q^{7} - 2 q^{16} - 2 q^{19} + 2 q^{28} + 2 q^{31} + 2 q^{37} + 2 q^{52} - 2 q^{67} - 2 q^{73} - 2 q^{76} - 2 q^{91} + 2 q^{97} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(117, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.1.j.a $2$ $0.058$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots$$