# Properties

 Label 152.1.u Level 152 Weight 1 Character orbit u Rep. character $$\chi_{152}(35,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 6 Newforms 1 Sturm bound 20 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 152.u (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$152$$ Character field: $$\Q(\zeta_{18})$$ Newforms: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(152, [\chi])$$.

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q - 3q^{3} - 3q^{6} - 3q^{8} - 3q^{9} + O(q^{10})$$ $$6q - 3q^{3} - 3q^{6} - 3q^{8} - 3q^{9} + 6q^{18} + 6q^{22} - 3q^{24} + 3q^{27} - 3q^{33} - 3q^{36} - 3q^{38} - 3q^{41} + 6q^{44} + 6q^{48} - 3q^{49} - 3q^{50} + 3q^{51} - 3q^{54} - 3q^{59} - 3q^{64} - 3q^{66} - 3q^{67} + 3q^{68} + 6q^{72} + 6q^{73} + 3q^{81} - 3q^{82} - 3q^{97} + 3q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(152, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
152.1.u.a $$6$$ $$0.076$$ $$\Q(\zeta_{18})$$ $$D_{9}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$$