Properties

 Label 93.1.l Level $93$ Weight $1$ Character orbit 93.l Rep. character $\chi_{93}(2,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $4$ Newform subspaces $1$ Sturm bound $10$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$93 = 3 \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 93.l (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$93$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(93, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

Trace form

 $$4 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10})$$ $$4 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} - 2 q^{13} - q^{16} - 2 q^{19} + 3 q^{21} + 4 q^{25} - q^{27} + 3 q^{28} - q^{31} + 4 q^{36} - 2 q^{37} + 3 q^{39} + 3 q^{43} - q^{48} - 3 q^{49} - 2 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{63} - q^{64} - 2 q^{67} - 2 q^{73} - q^{75} + 3 q^{76} + 3 q^{79} - q^{81} - 2 q^{84} + q^{91} - q^{93} + 3 q^{97} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(93, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
93.1.l.a $4$ $0.046$ $$\Q(\zeta_{10})$$ $D_{5}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$$